Sequences

392,541 sequences

a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=2, a(2)=1, and a(3)=3.A024961
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=2, a(2)=1, and a(3)=3.
a(n) = s(n+3)/3, where s is A024961.A024962
a(n) = s(n+3)/3, where s is A024961.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=3, a(2)=1, and a(3)=2.A024963
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=3, a(2)=1, and a(3)=2.
a(n) = s(n+3)/2, where s is A024963.A024964
a(n) = s(n+3)/2, where s is A024963.
a(n) = Sum(a(2i-1)*a(n-2i+1), i = 1,2,...,[ (n+2)/4 ]).A024965
a(n) = Sum(a(2i-1)*a(n-2i+1), i = 1,2,...,[ (n+2)/4 ]).
7 times triangular numbers: 7*n*(n+1)/2.A024966
7 times triangular numbers: 7*n*(n+1)/2.
Positions of primes in A003072.A024967
Positions of primes in A003072.
Positions of even numbers in A003072.A024968
Positions of even numbers in A003072.
Positions of odd numbers in A003072.A024969
Positions of odd numbers in A003072.
a(n) = position of 3*n^3 in A003072.A024970
a(n) = position of 3*n^3 in A003072.
a(n) = position of n^3 + 9 in A003072.A024971
a(n) = position of n^3 + 9 in A003072.
a(n) = position of n^3 + (n+1)^3 + (n+2)^3 in A003072.A024972
a(n) = position of n^3 + (n+1)^3 + (n+2)^3 in A003072.
Sum of three distinct positive cubes, including repetitions (first differs from A024975 at 1009).A024973
Sum of three distinct positive cubes, including repetitions (first differs from A024975 at 1009).
Numbers that are the sum of 3 distinct positive cubes in 2 or more ways.A024974
Numbers that are the sum of 3 distinct positive cubes in 2 or more ways.
Sums of three distinct positive cubes.A024975
Sums of three distinct positive cubes.
Positions of primes in A024975 (sums of three distinct cubes).A024976
Positions of primes in A024975 (sums of three distinct cubes).
Positions of even numbers in A024975.A024977
Positions of even numbers in A024975.
Positions of odd numbers in A024975.A024978
Positions of odd numbers in A024975.
Position of n^3 + 9 in A024975.A024979
Position of n^3 + 9 in A024975.
a(n) = position of n^3 + (n+1)^3 + (n+2)^3 in A024975.A024980
a(n) = position of n^3 + (n+1)^3 + (n+2)^3 in A024975.
Numbers that are the sum of 3 positive cubes, including repetitions.A024981
Numbers that are the sum of 3 positive cubes, including repetitions.
Coordination sequence T1 for Zeolite Code IFR.A024982
Coordination sequence T1 for Zeolite Code IFR.
Coordination sequence T2 for Zeolite Code IFR.A024983
Coordination sequence T2 for Zeolite Code IFR.
Coordination sequence T3 for Zeolite Code IFR.A024984
Coordination sequence T3 for Zeolite Code IFR.
Coordination sequence T4 for Zeolite Code IFR.A024985
Coordination sequence T4 for Zeolite Code IFR.
Coordination sequence T1 for Zeolite Code MWW.A024986
Coordination sequence T1 for Zeolite Code MWW.
Coordination sequence T2 for Zeolite Code MWW.A024987
Coordination sequence T2 for Zeolite Code MWW.
Coordination sequence T3 for Zeolite Code MWW.A024988
Coordination sequence T3 for Zeolite Code MWW.
Coordination sequence T4 for Zeolite Code MWW.A024989
Coordination sequence T4 for Zeolite Code MWW.
Coordination sequence T5 for Zeolite Code MWW.A024990
Coordination sequence T5 for Zeolite Code MWW.
Coordination sequence T6 for Zeolite Code MWW.A024991
Coordination sequence T6 for Zeolite Code MWW.
Coordination sequence T7 for Zeolite Code MWW.A024992
Coordination sequence T7 for Zeolite Code MWW.
Coordination sequence T8 for Zeolite Code MWW.A024993
Coordination sequence T8 for Zeolite Code MWW.
Number of periodic partitions of n: each part occurs more than once and the same number of times.A024994
Number of periodic partitions of n: each part occurs more than once and the same number of times.
Least k such that k has more periodic partitions than does any j less than k (cf. A024994).A024995
Least k such that k has more periodic partitions than does any j less than k (cf. A024994).
Triangular array, read by rows: second differences in n,n direction of trinomial array A027907.A024996
Triangular array, read by rows: second differences in n,n direction of trinomial array A027907.
a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0 = s(n), |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3. Also a(n) = T(n,n), where T is the array defined in A024996.A024997
a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0 = s(n), |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3. Also a(n) = T(n,n), where T is the array defined in A024996.
a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 1. Also a(n) = T(n,n-1), where T is the array defined in A024996.A024998
a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 1. Also a(n) = T(n,n-1), where T is the array defined in A024996.
Expansion of 1/((1-x)(1-8x)(1-10x)(1-11x)).A024999
Expansion of 1/((1-x)(1-8x)(1-10x)(1-11x)).
a(1) = 3; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.A025000
a(1) = 3; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.
a(1) = 5; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.A025001
a(1) = 5; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.
a(1) = 7; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.A025002
a(1) = 7; a(n+1) = a(n)-th nonprime, where nonprimes begin at 0.
a(1) = 2; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.A025003
a(1) = 2; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.
a(1) = 3; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.A025004
a(1) = 3; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.
a(1) = 5; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.A025005
a(1) = 5; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.
a(1) = 7; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.A025006
a(1) = 7; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1.
Expansion of 1/((1-x)(1-8x)(1-10x)(1-12x)).A025007
Expansion of 1/((1-x)(1-8x)(1-10x)(1-12x)).
Expansion of 1/((1-x)(1-8x)(1-11x)(1-12x)).A025008
Expansion of 1/((1-x)(1-8x)(1-11x)(1-12x)).
Expansion of 1/((1-x)(1-9x)(1-10x)(1-11x)).A025009
Expansion of 1/((1-x)(1-9x)(1-10x)(1-11x)).
a(1) = 5; a(n+1) = a(n)-th nonprime, where nonprimes begin at 4.A025010
a(1) = 5; a(n+1) = a(n)-th nonprime, where nonprimes begin at 4.