22140

Appears in sequences

• Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.at n=40A000330
• High-temperature series in v = tanh(J/kT) for susceptibility for the Ising model on honeycomb structure.at n=15A002910
• Number of primitive (aperiodic, or Lyndon) asymmetric rhythm cycles: ones having no nontrivial shift automorphism.at n=11A006575
• Even square pyramidal numbers.at n=19A015222
• Number of distinct 'failure tables' for a string of length n.at n=12A022543
• a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = floor(n/2), s = (odd natural numbers).at n=39A025112
• Numbers having four 3's in base 9.at n=12A043468
• a(n) = Sum_{k=1..n, gcd(n,k) = 1} k^2.at n=40A053818
• Number of positive integers <= 2^n of the form x^2 + 5*y^2.at n=17A054150
• Consider the line segment in R^n from the origin to the point P=(1,2,3,...,n); let d = squared distance to this line from the closest point of Z^n (excluding the endpoints). Sequence gives d times P.P.at n=39A059774
• Square pyramorphic numbers: suppose the k-th square pyramidal number S(k) (A000330) ends in k; sequence gives value of S(k).at n=3A060204
• Number T(n,m) of n X m matrices over {0,1,2} with all row and column sums equal to 1 or 2, m=0,..,2*n.at n=22A062154
• Number T(n,m) of n X m matrices over {0,1,2} with all row and column sums equal to 1 or 2, m=0,..,2*n.at n=40A062154
• Numbers n such that h(n) = 3 h(n-1) where h(n) is the length of the sequence {n, f(n), f(f(n)), ...., 1} in the Collatz (or 3x + 1) problem. (The earliest "1" is meant.)at n=21A078420
• Number of ways to partition the set of divisors of the n-th abundant number into three subsets such that their sums form an integer triangle.at n=20A091235
• Least area/6 of primitive Pythagorean triangles with odd leg 2n+1.at n=39A096893
• Sequence and first differences include all square numbers exactly once.at n=39A109678
• a(0)=0; then a(4*k+1)=a(4*k)+(4*k+1)^2, a(4*k+2)=a(4*k+1)+(4*k+3)^2, a(4*k+3)=a(4*k+2)+(4*k+2)^2, a(4*k+4)=a(4*k+3)+(4*k+4)^2.at n=40A115391
• a(n) = Sum_{k=1..phi(n)} k*t(k), where t(k) is the k-th positive integer which is coprime to n and phi(n) is the number of positive integers which are <= n and are coprime to n.at n=40A135324
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 1)}.at n=9A148953