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A182735 Number of parts in all partitions of 2n+1 that do not contain 1 as a part.

%I A182735 #15 Oct 29 2015 08:10:36
%S A182735 0,1,3,8,20,41,80,153,271,469,795,1305,2102,3336,5190,7968,12090,
%T A182735 18104,26821,39371,57220,82472,117958,167405,235945,330425,459803,
%U A182735 636142,875307,1197983,1631470,2211377,2983695,4008386,5362831,7146335,9486834,12548085,16538651
%N A182735 Number of parts in all partitions of 2n+1 that do not contain 1 as a part.
%H A182735 Alois P. Heinz, <a href="/A182735/b182735.txt">Table of n, a(n) for n = 0..1000</a>
%p A182735 b:= proc(n,i) option remember; local p,q;
%p A182735       if n<0 then [0,0]
%p A182735     elif n=0 then [1,0]
%p A182735     elif i<2 then [0,0]
%p A182735     else p, q:= b(n,i-1), b(n-i,i);
%p A182735         [p[1]+q[1], p[2]+q[2]+q[1]]
%p A182735       fi
%p A182735     end:
%p A182735 a:= n-> b(2*n+1, 2*n+1)[2]:
%p A182735 seq(a(n), n=0..35);  # _Alois P. Heinz_, Dec 03 2010
%t A182735 b[n_, i_] := b[n, i] = Module[{p, q}, Which[n<0, {0, 0}, n == 0, {1, 0}, i < 2, {0, 0}, True, {p, q} = {b[n, i-1], b[n-i, i]}; {p[[1]] + q[[1]], p[[2]] + q[[2]] + q[[1]]}]]; a[n_] := b[2*n+1, 2*n+1][[2]]; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Oct 29 2015, after _Alois P. Heinz_ *)
%Y A182735 Cf. A135010, A138121, A182734, A182743, A182747. Bisection (odd part) of A138135.
%K A182735 nonn
%O A182735 0,3
%A A182735 _Omar E. Pol_, Dec 03 2010
%E A182735 More terms from _Alois P. Heinz_, Dec 03 2010