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A099129 Let T(n) be the n-th triangular number n*(n+1)/2; then a(n) = n-th iteration T(T(T(...(n)))). 2
1, 6, 231, 1186570, 347357071281165, 2076895351339769460477611370186681, 143892868802856286225154411591351342616163027795335641150249224655238508171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The growth of this sequence is faster than exponential. This can be derived from the exponential generating function for triangular numbers: g(x) = (1 + 2x + x^2/2)*e^x = 1 + 3x/1! + 6x^2/2! + 10x^3/3! + 15x^4/4! + 21x^5/5! + ...

The next term, a(8), has 162 digits. - Harvey P. Dale, May 29 2013

REFERENCES

J. V. Post, "Iterated Triangular Numbers", preprint.

J. V. Post, "Iterated Polygonal Numbers", preprint.

LINKS

Table of n, a(n) for n=0..6.

FORMULA

a(n) = A007501(n, n)

The sequence grows like O(n^2^n*1/2^n). This can be derived from the growth O(n^2*1/2) of the triangle sum by iteration. - Hieronymus Fischer, Jan 21 2006

EXAMPLE

a(3) = 231 because we can write the 3-time iterated expression on T(3), the triangular number sequence n*(n+1)/2, namely: T(T(T(3))) = 231.

MATHEMATICA

Table[Nest[(#(#+1))/2&, n, n], {n, 8}] (* Harvey P. Dale, May 29 2013 *)

PROG

(PARI) a(n) = my(k = n); for (j=1, n, k = k*(k+1)/2; ); k; \\ Michel Marcus, Jan 01 2017

CROSSREFS

Cf. A000217, A007501, A058009 (analog with primes).

Sequence in context: A286314 A099124 A172862 * A286392 A221926 A324232

Adjacent sequences:  A099126 A099127 A099128 * A099130 A099131 A099132

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 14 2004

STATUS

approved

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Last modified December 6 07:11 EST 2019. Contains 329785 sequences. (Running on oeis4.)