cp's OEIS Frontend

A025159 Number of partitions of n with distinct parts p(i) such that if i != j, then |p(i) - p(j)| >= 5.

%I A025159 #12 Jan 02 2016 12:25:02
%S A025159 1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,10,12,13,15,17,19,21,24,26,29,
%T A025159 32,35,38,42,46,50,55,60,66,72,79,86,95,103,113,123,135,146,160,173,
%U A025159 189,204,222,239,260,280,303,326,353,379,410,440,475,510,550,590,636,682
%N A025159 Number of partitions of n with distinct parts p(i) such that if i != j, then |p(i) - p(j)| >= 5.
%H A025159 Alois P. Heinz, <a href="/A025159/b025159.txt">Table of n, a(n) for n = 1..1000</a>
%F A025159 G.f.: Sum(x^(5/2*k^2-3/2*k)/Product(1-x^i, i=1..k), k=1..infinity). - _Vladeta Jovovic_, Aug 12 2004
%F A025159 a(n) ~ c^(1/4) * r * exp(2*sqrt(c*n)) / (2*sqrt(Pi*(1-r)*(5-4*r)) * n^(3/4)), where r = 0.754877666246692760049508896358528691894606617772793143989... is the root of the equation r^5 + r = 1 and c = 5*log(r)^2/2 + polylog(2, 1-r) = 0.45973143655369174108251201834952526825516678... . - _Vaclav Kotesovec_, Jan 02 2016
%Y A025159 Cf. A003114, A025157-A025162.
%Y A025159 Column k=5 of A194543.
%K A025159 nonn
%O A025159 1,7
%A A025159 _Clark Kimberling_
%E A025159 More terms from _Vladeta Jovovic_, Aug 12 2004