31626

Appears in sequences

• Even triangular numbers with prime indices.at n=28A034955
• Triangular numbers which are also happy numbers (cf. A007770).at n=39A076712
• a(n)=b(n,n) with b(n,1)=n and b(n,k)=binomial(b(n,k-1),d(n,n-k+1)) for 1<k<=n, where d(n,i) are the divisors of n, d(i)<d(j), 1<=i<j<=A000005(n).at n=9A084678
• Triangular numbers in which the sum of the external digits equals the sum of the internal digits.at n=14A088289
• Triangular numbers that are sums of two consecutive primes.at n=28A111163
• Triangular numbers for which the sum of the digits is a heptagonal number.at n=29A117312
• Triangle read by rows. T(n,k) = binomial(n,k)*(binomial(n,k)-1)/2.at n=40A143418
• 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), (-1, 1, 1), (0, 0, 1), (1, 1, -1)}.at n=10A148457
• Triangle, read by rows, T(n, k) = A059481(n,k)*(A059481(n,k) - 1)/2.at n=19A171379
• Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 267", based on the 5-celled von Neumann neighborhood.at n=36A271085
• Number of sets of exactly n positive integers <= n+9 having a square element sum.at n=14A281972
• Number of maximal cliques in the n X n queen graph.at n=34A288947
• Sum over all partitions of n into distinct parts of the bitwise OR of the parts.at n=41A306924
• Triangular numbers (A000217) in A353729.at n=9A370520
• a(n) = Sum_{k=0..n} 2^(n-k) * binomial(4*n,k).at n=5A385498
• a(n) = Sum_{k=0..n-1} binomial(3*k+1,k) * binomial(3*n-3*k,n-k-1).at n=6A386617