A050548 Iterated triangular numbers with seed 7.

7, 28, 406, 82621, 3413156131, 5824817388998022646, 16964248807586870937449001943463431981, 143892868802856286225154411591351342616163027795335641150249224655238508171

Offset: 0

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 29 1999

Keywords

• nonn
• easy
• nice

Comments

a(8) has 149 digits. - Harvey P. Dale, May 08 2011

Links

• T. D. Noe, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A000217, A007501, A013589.

Cf. A050542, A050536, A050909.

Programs

Haskell

a050548 n = a050548_list !! n
a050548_list = iterate a000217 7

Mathematica

NestList[Binomial[#+1,2]&,7,10] (* Harvey P. Dale, May 08 2011 *)
t = {7}; Do[AppendTo[t, t[[-1]]*(1 + t[[-1]])/2], {9}] (* T. D. Noe, Mar 03 2014 *)

PARI

a(n)=my(k=7); for(i=1,n,k=binomial(k+1,2)); k \\ Charles R Greathouse IV, Mar 03 2014

Python

from itertools import accumulate
def f(an, _): return an*(an+1)//2
print(list(accumulate([7]*11, f))) # Michael S. Branicky, Jul 28 2021

Formula

a(n) = binomial(a(n-1)+1, 2), a(0)=7.

a(n) ~ 2 * c^(2^n), where c = 3.77579046114281148578572146955902030830005575599864345238... . - Vaclav Kotesovec, Dec 17 2014

Extensions

a(7) provided by Harvey P. Dale, May 08 2011