A086781 a(n) is the number of nonzero terms in the expansion of (x-y) * (x^2-y^2) * (x^3-y^3) * ... * (x^n-y^n).

1, 2, 4, 6, 7, 12, 14, 18, 25, 32, 36, 42, 53, 68, 64, 84, 97, 108, 126, 146, 161, 170, 192, 208, 229, 246, 274, 300, 333, 348, 372, 400, 427, 468, 492, 526, 561, 602, 626, 644, 691, 736, 772, 826, 869, 902, 930, 974, 1017, 1062, 1120, 1184, 1223, 1262, 1314, 1374, 1419, 1468, 1518, 1586, 1663, 1718, 1778, 1834, 1899, 1954, 2018

Offset: 0

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003

Keywords

• nonn

Comments

In the definition one can take y=1. - Emeric Deutsch, Jan 01 2008

Links

• Joerg Arndt, Table of n, a(n) for n = 0..1000
• Dorin Andrica and Ovidiu Bagdasar, On some results concerning the polygonal polynomials, Carpathian Journal of Mathematics (2019) Vol. 35, No. 1, 1-11.

Crossrefs

Cf. A000124, A086376.

Programs

Maple

a:=proc(n) options operator, arrow: nops(expand(product(x^j-y^j,j=1..n))) end proc: seq(a(n),n=0..50); # Emeric Deutsch, Jan 01 2008

Mathematica

Table[Length[Expand[Times@@(x^Range[n]-1)]],{n,50}] (* Harvey P. Dale, Mar 01 2012 *)

PARI

a(n)=#select(w->w, Vec(prod(k=1,n,1-'x^k))); \\ Joerg Arndt, Apr 12 2017

Extensions

More terms from Emeric Deutsch, Jan 01 2008

a(0)=1 prepended by Alois P. Heinz, Apr 12 2017