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

0, 0, 1, 3, 7, 15, 29, 53, 94, 160, 265, 430, 683, 1066, 1640, 2487, 3725, 5519, 8092, 11752, 16922, 24167, 34254, 48213, 67409, 93661, 129378, 177720, 242841, 330172, 446772, 601810, 807153, 1078081, 1434250, 1900860, 2510097, 3303003, 4331767, 5662539

Offset: 0

Author

Omar E. Pol, Dec 03 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

A182743. 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+1, 2*n+1):
seq(a(n), n=0..45);  # Alois P. Heinz, Dec 03 2010

Mathematica

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]]];
a[n_] := b[2n+1, 2n+1];
a /@ Range[0, 45] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)
Table[Count[Flatten[Select[IntegerPartitions[2 n+1],FreeQ[#,1]&]],2],{n,0,40}] (* Harvey P. Dale, Jan 28 2022 *)

Extensions

More terms from Alois P. Heinz, Dec 03 2010