A182735 Number of parts in all partitions of 2n+1 that do not contain 1 as a part.

0, 1, 3, 8, 20, 41, 80, 153, 271, 469, 795, 1305, 2102, 3336, 5190, 7968, 12090, 18104, 26821, 39371, 57220, 82472, 117958, 167405, 235945, 330425, 459803, 636142, 875307, 1197983, 1631470, 2211377, 2983695, 4008386, 5362831, 7146335, 9486834, 12548085, 16538651

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

Cf. A135010, A138121, A182734, A182743, A182747. Bisection (odd part) of A138135.

Programs

Maple

b:= proc(n,i) option remember; local p,q;
      if n<0 then [0,0]
    elif n=0 then [1,0]
    elif i<2 then [0,0]
    else p, q:= b(n,i-1), b(n-i,i);
        [p[1]+q[1], p[2]+q[2]+q[1]]
      fi
    end:
a:= n-> b(2*n+1, 2*n+1)[2]:
seq(a(n), n=0..35);  # Alois P. Heinz, Dec 03 2010

Mathematica

b[n_, i_] := b[n, i] = Module[{p, q}, Which[n<0, {0, 0}, n == 0, {1, 0}, i < 2, {0, 0}, True, {p, q} = {b[n, i-1], b[n-i, i]}; {p[[1]] + q[[1]], p[[2]] + q[[2]] + q[[1]]}]]; a[n_] := b[2*n+1, 2*n+1][[2]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Oct 29 2015, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Dec 03 2010