Sequences

Nicomachus triangle read by rows, T(n, k) = 2^(n - k)*3^k, for 0 <= k <= n.

a(n) = 4^(n+1) + 3*2^n + 1.

a(n) = 2^n - 3.

a(n) = 2^n - 45 with n>5, a(5)=1.

Triangle of numbers in which i-th row is {2^(i-j)*7^j, 0<=j<=i}; i >= 0.

Numbers of form 7^i*8^j with i, j >= 0, sorted.

Basic numbers used in Sedgewick-Incerpi upper bound for shell sort.

Continued fraction for ratio of small diagonal to side of regular 17-gon.

Increments used in Sedgewick-Incerpi upper bound for shell sort.

Primes p such that (p+1)/2 and (p+2)/3 are also primes.

Binary packing of Connell sequence (shifted once right).

Number of tetrahedra in largest triangulation of polygonal prism with regular polygonal base.

Size of maximal triangulation of an n-antiprism with regular polygonal base.

a(n) = least number not of form [ (a^2+b^2)/n ].

a(n) = least number not of form [ (a^2/n) ] + [ (b^2)/n ].

a(n) is the least number not of the form floor(k^2/n).

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

Number of binary rooted trees with n nodes and height at most 4.

Number of binary rooted trees with n nodes and height at most 5.

Number of binary rooted trees with n nodes and height at most 6.

Number of binary rooted trees with n nodes and height at most 7.

Number of binary rooted trees with n nodes and height at most 8.

Number of binary rooted trees with n nodes and height at most 9.

Number of binary rooted trees with n nodes and height exactly 4.

Number of binary rooted trees with n nodes and height exactly 5.

Number of binary rooted trees with n nodes and height exactly 6.

Number of binary rooted trees with n nodes and height exactly 7.

Number of binary rooted trees with n nodes and height exactly 8.

Number of binary rooted trees with n nodes and height exactly 9.

Number of binary rooted trees with n nodes and height exactly 10.

Number of binary rooted trees with n nodes and height exactly 11.

Number of binary rooted trees with n nodes and height exactly 12.

Triangle of coefficients of generating function of binary rooted trees of height at most n.

a(n) = n! in binary.

Sorting numbers: minimal number of comparisons needed to sort n elements.

a(n) = a(n-2) + 2*a(n-3) + a(n-4).

Triangle of coefficients of generating function of 4-ary rooted trees of height at most n.

Triangle of coefficients of generating function of 5-ary rooted trees of height at most n.

Triangle of coefficients of generating function of 6-ary rooted trees of height at most n.

Number of 4-ary rooted trees with n nodes and height at most 4.

Number of 4-ary rooted trees with n nodes and height at most 5.