A160976 - OEIS

%I #19 Feb 06 2024 09:48:52

%S 1,0,0,0,0,0,1,1,1,1,1,1,2,1,2,1,2,1,4,2,4,4,5,4,9,6,8,9,11,9,16,12,

%T 16,16,18,18,27,21,27,28,34,31,47,39,50,50,60,57,81,72,88,89,105,101,

%U 136,124,153,151,176,171,222,205,246,252,287,281,353,334,392,401,460,453,559,534,620,636

%N Number of partitions of n where every part appears at least 6 times.

%H Seiichi Manyama, <a href="/A160976/b160976.txt">Table of n, a(n) for n = 0..5000</a> (terms 1..1000 from R. H. Hardin)

%F a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-6*x)) dx = -1.055135119523138524396962100839537485211520908123400469186... . - _Vaclav Kotesovec_, Jan 05 2016

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       b(n, i-1)+add(b(n-i*j, i-1), j=6..n/i)))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..75);  # _Alois P. Heinz_, Feb 06 2024

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(6*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 0,13

%A _R. H. Hardin_, Jun 01 2009

%E a(0)=1 prepended by _Seiichi Manyama_, Feb 06 2024