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

0, 1, 2, 4, 8, 15, 27, 48, 82, 137, 225, 362, 572, 892, 1370, 2078, 3117, 4624, 6791, 9885, 14263, 20416, 29007, 40921, 57345, 79864, 110565, 152211, 208435, 283982, 385048, 519695, 698346, 934477, 1245439, 1653485, 2187108, 2882686, 3786497, 4957324, 6469625

Offset: 0

Author

Omar E. Pol, Dec 03 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, and Gideon Vos, Large-N correlation functions in N = 2 superconformal QCD, arXiv preprint arXiv:1610.07612 [hep-th], 2016.

Crossrefs

Cf. A182742. Bisection of A182712.

Programs

Maple

b:= proc(n,i) option remember; local r;
      if n<=0 or i<2 then 0
    elif i=2 then `if`(irem(n,2,'r')=0,r,0)
    else b(n,i-1) +b(n-i,i)
      fi
    end:
a:= n-> b(2*n,2*n):
seq(a(n), n=0..40);  # Alois P. Heinz, Dec 03 2010

Mathematica

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 *)

Extensions

More terms from Alois P. Heinz, Dec 03 2010