A084376 G.f.: (1+x)/Product_{m>0} (1 - x^m).

1, 2, 3, 5, 8, 12, 18, 26, 37, 52, 72, 98, 133, 178, 236, 311, 407, 528, 682, 875, 1117, 1419, 1794, 2257, 2830, 3533, 4394, 5446, 6728, 8283, 10169, 12446, 15191, 18492, 22453, 27193, 32860, 39614, 47652, 57200, 68523, 81921, 97757, 116435, 138436

Offset: 0

Author

Vladeta Jovovic, Jun 23 2003

Keywords

• nonn

Links

• Robert Price, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A052816.

Programs

Maple

seq(numbpart(k)+numbpart(k+1), k=0..43); # Zerinvary Lajos, Jun 06 2007

Mathematica

Table[PartitionsP[n] + PartitionsP[n - 1], {n, 0, 44}] (* Robert Price, May 18 2020 *)

Formula

a(n) = A000041(n) + A000041(n-1), n>0.

a(n) ~ exp(sqrt(2*n/3)*Pi)/(2*sqrt(3)*n) * (1 - (sqrt(3/2)/Pi + 13*Pi/(24*sqrt(6)))/sqrt(n) + (13/16 + 313*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016