A281081 Expansion of Product_{k>=0} (1 + x^(3*k*(k+1)/2+1)).

1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 3, 1, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 3, 1, 0, 0, 1, 2

Offset

0,47

Comments

Number of partitions of n into distinct centered triangular numbers (A005448).

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Centered Triangular Number

Index entries for sequences related to centered polygonal numbers

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=0} (1 + x^(3*k*(k+1)/2+1)).

Example

a(46) = 2 because we have [46] and [31, 10, 4, 1].

Mathematica

nmax = 105; CoefficientList[Series[Product[1 + x^(3 k (k + 1)/2 + 1), {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A005448, A024940, A279278, A280950, A281082, A281083, A281084.

Sequence in context: A319138 A349396 A330462 * A103344 A123484 A008626

Adjacent sequences: A281078 A281079 A281080 * A281082 A281083 A281084

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 14 2017

Status

approved