A066370 Quadruply triangular numbers.

0, 1, 231, 26796, 1186570, 26357430, 359026206, 3413156131, 24666759216, 143717956515, 703974775735, 2989908659661, 11270904497931, 38398515291136, 119929709686710, 347357071281165, 941718655098991, 2408309883851256, 5847191602173306, 13551450210950905

Offset

0,3

Comments

See sequences A000217, A002817 and A064322 for triangular, doubly triangular and triply triangular numbers, respectively.

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Formula

a(n) = n*(n + 1)*(n^2 + n + 2)*(n^4 + 2*n^3 + 3*n^2 + 2*n + 8)*(n^8 + 4*n^7 + 10*n^6 + 16*n^5 + 25*n^4 + 28*n^3 + 28*n^2 + 16*n + 128)/32768.

a(n) = A064322(n)*(A064322(n) + 1)/2 = A000217(A000217(A000217(A000217(n)))).

Example

a(2)=231 as A000217(A000217(A000217(A000217(2))))=231 is the second quadruply-triangular number.

Mathematica

f[n_] := n(n + 1)/2; Table[ Nest[f, n, 4], {n, 0, 17}] (* Robert G. Wilson v, Jun 30 2004 *)

Crossrefs

Sequence in context: A362429 A201957 A152500 * A139412 A027551 A172861

Adjacent sequences: A066367 A066368 A066369 * A066371 A066372 A066373

Keyword

nonn

Author

Brian Bayerle (bbayer03(AT)providence.edu), Dec 22 2001

Status

approved