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