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A064322 Triply triangular numbers. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..400

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) Tri(n)= { n*(n + 1)/2 } { for (n=0, 400, write("b064322.txt", n, " ", 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

AUTHOR

Henry Bottomley, Oct 15 2001

STATUS

approved

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Last modified March 25 07:12 EDT 2019. Contains 321468 sequences. (Running on oeis4.)