cp's OEIS Frontend

A182734 Number of parts in all partitions of 2n that do not contain 1 as a part.

%I A182734 #21 Jun 01 2021 08:06:35
%S A182734 0,1,3,8,17,34,68,123,219,382,642,1055,1713,2713,4241,6545,9950,14953,
%T A182734 22255,32752,47774,69104,99114,141094,199489,280096,390836,542170,
%U A182734 747793,1025912,1400425,1902267,2572095,3462556,4641516,6196830,8241460,10919755,14416885
%N A182734 Number of parts in all partitions of 2n that do not contain 1 as a part.
%C A182734 Essentially this is a bisection (even part) of A138135.
%H A182734 Alois P. Heinz, <a href="/A182734/b182734.txt">Table of n, a(n) for n = 0..1000</a>
%p A182734 b:= proc(n,i) option remember; local p,q;
%p A182734       if n<0 then [0,0]
%p A182734     elif n=0 then [1,0]
%p A182734     elif i=1 then [0,0]
%p A182734     else p, q:= b(n,i-1), b(n-i,i);
%p A182734          [p[1]+q[1], p[2]+q[2]+q[1]]
%p A182734       fi
%p A182734     end:
%p A182734 a:= n-> b(2*n, 2*n)[2]:
%p A182734 seq(a(n), n=0..35);  # _Alois P. Heinz_, Dec 03 2010
%t A182734 Table[Length[Flatten[DeleteCases[IntegerPartitions[2n],_?(MemberQ[ #,1]&)]]], {n,0,40}] (* _Harvey P. Dale_, Aug 08 2013 *)
%t A182734 b[n_] := DivisorSigma[0, n]-1+Sum[(DivisorSigma[0, k]-1)*(PartitionsP[n-k] - PartitionsP[n-k-1]), {k, 1, n-1}]; a[0] = 0; a[n_] := b[2n]; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Oct 07 2015 *)
%Y A182734 Cf. A135010, A138121, A138135, A182742.
%K A182734 nonn
%O A182734 0,3
%A A182734 _Omar E. Pol_, Dec 03 2010
%E A182734 More terms from _Alois P. Heinz_, Dec 03 2010