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A182717 Number of 2's in all partitions of 2n+1 that do not contain 1 as a part.

%I A182717 #22 Jan 28 2022 12:06:29
%S A182717 0,0,1,3,7,15,29,53,94,160,265,430,683,1066,1640,2487,3725,5519,8092,
%T A182717 11752,16922,24167,34254,48213,67409,93661,129378,177720,242841,
%U A182717 330172,446772,601810,807153,1078081,1434250,1900860,2510097,3303003,4331767,5662539
%N A182717 Number of 2's in all partitions of 2n+1 that do not contain 1 as a part.
%H A182717 Alois P. Heinz, <a href="/A182717/b182717.txt">Table of n, a(n) for n = 0..1000</a>
%p A182717 b:= proc(n,i) option remember; local r;
%p A182717       if n<=0 or i<2 then 0
%p A182717     elif i=2 then `if`(irem(n,2,'r')=0,r,0)
%p A182717     else b(n,i-1) +b(n-i,i)
%p A182717       fi
%p A182717     end:
%p A182717 a:= n-> b(2*n+1, 2*n+1):
%p A182717 seq(a(n), n=0..45);  # _Alois P. Heinz_, Dec 03 2010
%t A182717 b[n_, i_] := b[n, i] = If[n <= 0 || i < 2, 0, If[i == 2, If[Mod[n, 2] == 0, Quotient[n, 2], 0], b[n, i-1] + b[n-i, i]]];
%t A182717 a[n_] := b[2n+1, 2n+1];
%t A182717 a /@ Range[0, 45] (* _Jean-François Alcover_, Nov 11 2020, after _Alois P. Heinz_ *)
%t A182717 Table[Count[Flatten[Select[IntegerPartitions[2 n+1],FreeQ[#,1]&]],2],{n,0,40}] (* _Harvey P. Dale_, Jan 28 2022 *)
%Y A182717 A182743. Bisection of A182712.
%K A182717 nonn
%O A182717 0,4
%A A182717 _Omar E. Pol_, Dec 03 2010
%E A182717 More terms from _Alois P. Heinz_, Dec 03 2010