A162500 Expansion of the polynomial (1-x^3) * (1-x^6) * (1-x^9) / (1-x)^3.

1, 3, 6, 9, 12, 15, 17, 18, 18, 17, 15, 12, 9, 6, 3, 1

Offset: 0

Author

N. J. A. Sloane, Dec 02 2009

Keywords

• nonn
• fini
• full

Comments

This is a row of the triangle A162499.

Only finitely many terms are nonzero.

Crossrefs

Cf. A162499.

Programs

Magma

m:=16; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)/(1-x)^3)); /* complete row without zeros */ // G. C. Greubel, Jul 06 2018

Maple

m:=3: seq(coeff(series(mul((1-x^(3*i)),i=1..m)/(1-x)^m, x,n+1),x,n),n=0..16); # Muniru A Asiru, Jul 07 2018

Mathematica

CoefficientList[ Series[Times @@ (1 - x^(3 Range@3))/(1 - x)^3, {x, 0, 40}], x] (* Wesley Ivan Hurt, Sep 13 2014 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

PARI

x='x+O('x^16); Vec((1-x^3)*(1-x^6)*(1-x^9)/(1-x)^3) \\ G. C. Greubel, Jul 06 2018