A291553 Column 3 of A060244.

0, 0, 1, 2, 4, 8, 13, 22, 35, 54, 81, 121, 174, 250, 352, 491, 675, 924, 1246, 1674, 2226, 2944, 3862, 5046, 6541, 8449, 10846, 13869, 17641, 22365, 28214, 35485, 44443, 55494, 69036, 85650, 105894, 130594, 160561, 196923, 240847, 293907, 357722, 434477, 526448

Offset: 1

Author

Vaclav Kotesovec, Aug 26 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060244, A024786.

Programs

Mathematica

nmax = 50; col = 3; Flatten[{0, 0, CoefficientList[Coefficient[Normal[Series[Product[Product[1/(1 - x^(i - j)*y^j), {j, 0, i}], {i, 2, nmax + col}], {x, 0, col}, {y, 0, nmax}]], x^col], y]}]
nmax = 50; Rest[CoefficientList[Series[(x^3 * (1 + x - x^4))/((1-x)^2 * (1+x) * (1 + x + x^2)) / QPochhammer[x], {x, 0, nmax}], x]]
Table[Sum[(Floor[k/2] - Floor[(k-1)/3]) * PartitionsP[n-k], {k, 3, n}], {n, 1, 50}]

Formula

G.f.: x^3 * (1 + x - x^4) / ((1 - x)^2 * (1 + x) * (1 + x + x^2)) * Product_{k>=1} 1/(1 - x^k).

a(n) = Sum_{k=3..n} (floor(k/2) - floor((k-1)/3)) * A000041(n-k).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*Pi^2).

a(n) ~ n * A000041(n) / Pi^2.