A182734 Number of parts in all partitions of 2n that do not contain 1 as a part.

0, 1, 3, 8, 17, 34, 68, 123, 219, 382, 642, 1055, 1713, 2713, 4241, 6545, 9950, 14953, 22255, 32752, 47774, 69104, 99114, 141094, 199489, 280096, 390836, 542170, 747793, 1025912, 1400425, 1902267, 2572095, 3462556, 4641516, 6196830, 8241460, 10919755, 14416885

Offset: 0

Author

Omar E. Pol, Dec 03 2010

Keywords

• nonn

Comments

Essentially this is a bisection (even part) of A138135.

Links

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

Crossrefs

Cf. A135010, A138121, A138135, A182742.

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=1 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, 2*n)[2]:
seq(a(n), n=0..35);  # Alois P. Heinz, Dec 03 2010

Mathematica

Table[Length[Flatten[DeleteCases[IntegerPartitions[2n],?(MemberQ[ #,1]&)]]], {n,0,40}] (* _Harvey P. Dale, Aug 08 2013 *)
b[n_] := DivisorSigma[0, n]-1+Sum[(DivisorSigma[0, k]-1)*(PartitionsP[n-k] - PartitionsP[n-k-1]), {k, 1, n-1}]; a[0] = 0; a[n_] := b[2n]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Oct 07 2015 *)

Extensions

More terms from Alois P. Heinz, Dec 03 2010