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A182716 Number of 2's in all partitions of 2n that do not contain 1 as a part.

%I A182716 #26 Dec 04 2020 10:40:13
%S A182716 0,1,2,4,8,15,27,48,82,137,225,362,572,892,1370,2078,3117,4624,6791,
%T A182716 9885,14263,20416,29007,40921,57345,79864,110565,152211,208435,283982,
%U A182716 385048,519695,698346,934477,1245439,1653485,2187108,2882686,3786497,4957324,6469625
%N A182716 Number of 2's in all partitions of 2n that do not contain 1 as a part.
%H A182716 Alois P. Heinz, <a href="/A182716/b182716.txt">Table of n, a(n) for n = 0..1000</a>
%H A182716 Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, and Gideon Vos, <a href="http://arxiv.org/abs/1610.07612">Large-N correlation functions in N = 2 superconformal QCD</a>, arXiv preprint arXiv:1610.07612 [hep-th], 2016.
%p A182716 b:= proc(n,i) option remember; local r;
%p A182716       if n<=0 or i<2 then 0
%p A182716     elif i=2 then `if`(irem(n,2,'r')=0,r,0)
%p A182716     else b(n,i-1) +b(n-i,i)
%p A182716       fi
%p A182716     end:
%p A182716 a:= n-> b(2*n,2*n):
%p A182716 seq(a(n), n=0..40);  # _Alois P. Heinz_, Dec 03 2010
%t A182716 b[n_, i_] := b[n, i] = Module[{q, r}, Which[n <= 0 || i<2, 0, i==2, {q, r} = QuotientRemainder[n, 2]; If[r==0, q, 0], True, b[n, i-1]+b[n-i, i]]]; a[n_] := b[2n, 2n]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 21 2017, after _Alois P. Heinz_ *)
%Y A182716 Cf. A182742. Bisection of A182712.
%K A182716 nonn
%O A182716 0,3
%A A182716 _Omar E. Pol_, Dec 03 2010
%E A182716 More terms from _Alois P. Heinz_, Dec 03 2010