A225549 a(n) is the number of terms in the expansion of (x-y)*(x^4-y^4)*(x^9-y^9)*...*(x^(n^2)-y^(n^2)).

2, 4, 8, 16, 24, 40, 68, 103, 162, 236, 344, 453, 612, 790, 994, 1229, 1432, 1782, 2134, 2517, 2968, 3460, 3974, 4543, 5160, 5822, 6546, 7347, 8184, 9080, 10058, 11075, 12166, 13316, 14536, 15837, 17202, 18654, 20156, 21765, 23450, 25212, 27074, 29001, 31032, 33158, 35370, 37679, 40070, 42578

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com) and Robert G. Wilson v, May 10 2013

Keywords

• nonn

Comments

In the definition one can take y=1. Thus the sequence becomes the number of terms in the polynomial of the product{k=1..n} (1-x^(k^2)).

Crossrefs

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

Programs

Mathematica

a[n_] := Length@ ExpandAll@ Product[(1 - x^(k^2)), {k, n}]; Array[f, 40]

PARI

a(n)=my(P=prod(k=1,n,1-'x^k^2)); sum(i=0, poldegree(P), polcoeff(P,i)!=0) \\ Charles R Greathouse IV, May 10 2013