A222028 a(n) is the number of terms in the expansion of (x-y)(x^3-y^3)*(x^6-y^6)*(x^10-y^10)*...*(x^T_i-y^T_i), where T_i is the i-th triangular number.

2, 4, 8, 15, 28, 41, 66, 92, 132, 175, 232, 287, 360, 475, 570, 727, 852, 1009, 1220, 1397, 1646, 1891, 2154, 2441, 2772, 3121, 3508, 3891, 4334, 4791, 5282, 5797, 6376, 6983, 7618, 8285, 8984, 9713, 10500, 11319, 12182, 13093, 14028, 15023, 16064, 17157, 18276, 19447, 20680, 21953

Offset

1,1

Comments

In the definition one can take y=1. Thus the sequence becomes the number of terms in the polynomial of the product{k=0..n} (1-x^T_i), where G_i is the i-th triangular number.

Links

Table of n, a(n) for n=1..50.

Mathematica

f[n_] := Length@ ExpandAll@ Product[1 - x^(k (k + 1)/2), {k, n}]; Array[f, 50]

Crossrefs

Cf. A000124, A086781, A086795, A086796, A086817, A221991, A225549.

Sequence in context: A367223 A284275 A054159 * A338760 A056181 A101976

Adjacent sequences: A222025 A222026 A222027 * A222029 A222030 A222031

Keyword

nonn

Author

Robert G. Wilson v, May 12 2013

Status

approved