A051678 Square-pyramid-tree numbers: a(n) = sum(b(m),m=1..n), b(m) = 1^2, 1^2,2^2, 1^2,2^2,3^2,.. = (A002260)^2.

1, 2, 6, 7, 11, 20, 21, 25, 34, 50, 51, 55, 64, 80, 105, 106, 110, 119, 135, 160, 196, 197, 201, 210, 226, 251, 287, 336, 337, 341, 350, 366, 391, 427, 476, 540, 541, 545, 554, 570, 595, 631, 680, 744, 825, 826, 830, 839, 855, 880, 916, 965, 1029, 1110, 1210

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..5050

Formula

a(n * (n + 1)/2 + m) = 1/12 * n * (n + 2) * (n + 1)^2 + 1/6 * m * (m + 1) * (2 * m + 1) = A002415(n) + A000330(m), m = 0...n + 1, n = 1, 2, 3..

Mathematica

Table[n^2 (n^2 - 1)/12 + m (m + 1) (2 m + 1)/6, {n, 10}, {m, n}] // Flatten (* Ivan Neretin, May 22 2015 *)

Crossrefs

Cf. A002260, A000330, A002415.

Sequence in context: A174000 A241720 A224082 * A079906 A226814 A233419

Adjacent sequences: A051675 A051676 A051677 * A051679 A051680 A051681

Keyword

easy,nice,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)

Status

approved