A064322 Triply triangular numbers.

0, 1, 21, 231, 1540, 7260, 26796, 82621, 222111, 536130, 1186570, 2445366, 4747821, 8763391, 15487395, 26357430, 43398586, 69401871, 108140571, 164629585, 245433090, 359026206, 516216646, 730632651, 1019283825, 1403201800, 1908167976, 2565535896, 3413156131

Offset: 0

Author

Henry Bottomley, Oct 15 2001

Keywords

• nonn
• easy

Examples

			a(4) = 1540 because 4th triangular number is 10, 10th triangular number is 55 and 55th triangular number is 1540.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A000217, A002817, A066370.

Programs

Maple

a:= n-> ((k-> binomial(k+1,2))@@3)(n):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 19 2012

Mathematica

f[n_] := n(n + 1)/2; Table[ Nest[f, n, 3], {n, 0, 25}] (* Robert G. Wilson v, Jun 30 2004 *)

PARI

a(n) = { my(Tri(m)= m*(m + 1)/2); Tri(Tri(Tri(n))) } \\ Harry J. Smith, Sep 11 2009

Formula

a(n) = A000217(A000217(A000217(n))) = n*(n+1)*(n^2 + n + 2)*(n^4 + 2n^3 + 3n^2 + 2n + 8)/128 = A002817(n)*(A002817(n) + 1)/2.

G.f.: x*(1 + 12*x + 78*x^2 + 133*x^3 + 78*x^4 + 12*x^5 + x^6)/(1 - x)^9. - Colin Barker, Apr 19 2012