Sequences
392,541 sequences
- a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n+1/2, a>0, b>=0.A036711
a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n+1/2, a>0, b>=0.
- Erroneous version of A036706.A036712
Erroneous version of A036706.
- a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n+1/2, a>=0, 0<=b<a.A036713
a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n+1/2, a>=0, 0<=b<a.
- a(n)=number of Gaussian integers z=a+bi satisfying n-1/2<|z|<=n+1/2, a>=0, 0<=b<a.A036714
a(n)=number of Gaussian integers z=a+bi satisfying n-1/2<|z|<=n+1/2, a>=0, 0<=b<a.
- a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n+1/2, a>=0, 0<=b<=a.A036715
a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n+1/2, a>=0, 0<=b<=a.
- a(n)=number of Gaussian integers z=a+bi satisfying n-1/2<|z|<=n+1/2, a>=0, 0<=b<=a.A036716
a(n)=number of Gaussian integers z=a+bi satisfying n-1/2<|z|<=n+1/2, a>=0, 0<=b<=a.
- G.f. satisfies A(x) = 1 + x*cycle_index(Alt(4), A(x)).A036717
G.f. satisfies A(x) = 1 + x*cycle_index(Alt(4), A(x)).
- Number of rooted trees where each node has at most 4 children.A036718
Number of rooted trees where each node has at most 4 children.
- G.f. satisfies A(x) = 1 + x*cycle_index(Cyclic(4), A(x)).A036719
G.f. satisfies A(x) = 1 + x*cycle_index(Cyclic(4), A(x)).
- G.f. satisfies A(x) = 1 + x*cycle_index(Klein_4_group, A(x)).A036720
G.f. satisfies A(x) = 1 + x*cycle_index(Klein_4_group, A(x)).
- G.f. satisfies A(x) = 1 + x*cycle_index(Sym(5), A(x)).A036721
G.f. satisfies A(x) = 1 + x*cycle_index(Sym(5), A(x)).
- G.f. satisfies A(x) = 1 + x*cycle_index(Sym(6), A(x)).A036722
G.f. satisfies A(x) = 1 + x*cycle_index(Sym(6), A(x)).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4).A036723
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4)(5,6).A036724
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4)(5,6).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4)(5,6)(7,8).A036725
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4)(5,6)(7,8).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 3 generated by (1,2,3)(4,5,6).A036726
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 3 generated by (1,2,3)(4,5,6).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 5 generated by (1,2,3,4,5).A036727
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 5 generated by (1,2,3,4,5).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 7 generated by (1,2,...,7).A036728
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 7 generated by (1,2,...,7).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 11 generated by (1,2,...,11).A036729
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 11 generated by (1,2,...,11).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 13 generated by (1,2,...,13).A036730
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 13 generated by (1,2,...,13).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 17 generated by (1,2,...,17).A036731
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 17 generated by (1,2,...,17).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 19 generated by (1,2,...,19).A036732
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 19 generated by (1,2,...,19).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 23 generated by (1,2,...,23).A036733
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 23 generated by (1,2,...,23).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 29 generated by (1,2,...,29).A036734
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 29 generated by (1,2,...,29).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 31 generated by (1,2,...,31).A036735
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 31 generated by (1,2,...,31).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 37 generated by (1,2,...,37).A036736
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 37 generated by (1,2,...,37).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 41 generated by (1,2,...,41).A036737
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 41 generated by (1,2,...,41).
- G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 43 generated by (1,2,...,43).A036738
G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 43 generated by (1,2,...,43).
- a(n) = (n!)^n+1.A036739
a(n) = (n!)^n+1.
- a(n) = (n!)^n.A036740
a(n) = (n!)^n.
- Values increase, Roman numerals increase lexicographically.A036741
Values increase, Roman numerals increase lexicographically.
- Numbers <= 3999 sorted in Roman numeral lexicographic order.A036742
Numbers <= 3999 sorted in Roman numeral lexicographic order.
- Numbers <= 3999 sorted in Roman numeral reverse lexicographic order.A036743
Numbers <= 3999 sorted in Roman numeral reverse lexicographic order.
- Penholodigital squares: squares containing each of the digits 1..9 exactly once.A036744
Penholodigital squares: squares containing each of the digits 1..9 exactly once.
- Squares including each digit exactly once.A036745
Squares including each digit exactly once.
- Numbers with "long" representations in Roman notation: given by last n letters from ...MMMDCCCLXXXVIII.A036746
Numbers with "long" representations in Roman notation: given by last n letters from ...MMMDCCCLXXXVIII.
- The numbers 0-100 in English lexicographic order.A036747
The numbers 0-100 in English lexicographic order.
- Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 6.A036748
Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 6.
- Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 7.A036749
Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 7.
- Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 7.A036750
Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 7.
- Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 8.A036751
Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 8.
- Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 8.A036752
Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 8.
- Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 9.A036753
Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 9.
- Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 9.A036754
Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 9.
- Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 10.A036755
Number of strings of n distinct digits from 0-9 that are the last n digits of a square in base 10.
- Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 10.A036756
Number of strings of n distinct digits from 1-9 that are the last n digits of a square in base 10.
- Number of tree-like heptagonal systems.A036757
Number of tree-like heptagonal systems.
- Number of edge-rooted tree-like octagonal systems.A036758
Number of edge-rooted tree-like octagonal systems.
- Number of mirror-symmetrical edge-rooted tree-like octagonal systems.A036759
Number of mirror-symmetrical edge-rooted tree-like octagonal systems.
- Number of tree-like octagonal systems.A036760
Number of tree-like octagonal systems.