cp's OEIS Frontend

A319776 Number of partitions of 2n in which any two distinct parts differ by at least n.

%I A319776 #12 Jan 30 2022 02:34:34
%S A319776 1,2,4,6,8,9,14,13,17,20,23,22,31,28,33,38,40,39,49,45,54,57,58,57,70,
%T A319776 68,71,76,81,78,93,86,94,98,99,104,116,109,114,119,128,123,138,131,
%U A319776 140,149,146,145,162,158,166,168,173,170,185,184,193,194,195,194
%N A319776 Number of partitions of 2n in which any two distinct parts differ by at least n.
%H A319776 Vaclav Kotesovec, <a href="/A319776/b319776.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..2000 from Alois P. Heinz)
%F A319776 a(n) = A218698(2n,n).
%p A319776 g:= proc(n,i) option remember;
%p A319776       add(`if`(irem(n, j)=0, 1, 0), j=1..i)
%p A319776     end:
%p A319776 a:= proc(n) option remember; numtheory[tau](2*n)+
%p A319776       add(g(2*n-j, min(2*n-j, j-n)), j=n+1..2*n-1)
%p A319776     end: a(0):=1:
%p A319776 seq(a(n), n=0..100);
%t A319776 g[n_, i_] := g[n, i] = Sum[If[Mod[n, j] == 0, 1, 0], {j, 1, i}];
%t A319776 a[n_] := a[n] = DivisorSigma[0, 2n] + Sum[g[2n - j, Min[2n - j, j - n]], {j, n + 1, 2n - 1}]; a[0] = 1;
%t A319776 a /@ Range[0, 100] (* _Jean-François Alcover_, Dec 12 2020, after _Alois P. Heinz_ *)
%Y A319776 Cf. A218698.
%K A319776 nonn
%O A319776 0,2
%A A319776 _Alois P. Heinz_, Sep 27 2018