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

Author

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

Keywords

• nonn

Comments

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

Examples

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

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).

Programs

Mathematica

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

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)))).