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

0,3

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).

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000217, A002817, A066370.

Sequence in context: A320588 A020267 A188354 * A126902 A162646 A247615

Adjacent sequences: A064319 A064320 A064321 * A064323 A064324 A064325

Keyword

nonn,easy,changed

Author

Henry Bottomley, Oct 15 2001

Status

approved