A268346 Number of partitions of (3, n) into a sum of distinct pairs.

2, 5, 9, 17, 27, 42, 64, 93, 132, 185, 254, 343, 459, 605, 790, 1024, 1314, 1673, 2118, 2661, 3324, 4132, 5107, 6282, 7695, 9383, 11396, 13792, 16629, 19982, 23938, 28586, 34037, 40420, 47868, 56546, 66640, 78348, 91908, 107589, 125680, 146522, 170499, 198027

Offset

0,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ 3^(1/4) * n^(3/4) * exp(Pi*sqrt(n/3)) / Pi^3.

Mathematica

max=50; col=3; s1=Series[Product[(1+x^(n-k)*y^k), {n, 1, max+2}, {k, 0, n}], {y, 0, col}]//Normal; s2=Series[s1, {x, 0, max+1}]; a[n_]:=SeriesCoefficient[s2, {x, 0, n}, {y, 0, col}]; Table[a[n], {n, 0, max}] (* after Jean-François Alcover *)
nmax = 50; CoefficientList[Series[((2 + x - x^2 - x^3 - x^4 + x^5) / ((1 - x)*(1 - x^2)*(1 - x^3))) * Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Column 3 of A054242.

Sequence in context: A308760 A342854 A062492 * A165271 A308827 A139672

Adjacent sequences: A268343 A268344 A268345 * A268347 A268348 A268349

Keyword

nonn

Author

Vaclav Kotesovec, Feb 02 2016

Status

approved