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A268346
Number of partitions of (3, n) into a sum of distinct pairs.
3
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 02 2016
STATUS
approved