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G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) / (1-x)^4.
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%I #19 Sep 08 2022 08:45:46

%S 1,4,10,19,31,46,63,81,99,116,131,143,151,154,151,143,131,116,99,81,

%T 63,46,31,19,10,4,1

%N G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) / (1-x)^4.

%C This is a row of the triangle in A162499. Only finitely many terms are nonzero.

%F Euler transform of period 12 sequence [4, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1]. - _Michael Somos_, Aug 02 2018

%p m:=4: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..26); # _Muniru A Asiru_, Jul 07 2018

%t CoefficientList[ Series[Times @@ (1 - x^(3*Range@4))/(1 - x)^4, {x, 0, 40}], x] (* _Harvey P. Dale_, Feb 05 2012 and slightly modified by _Robert G. Wilson v_, Jul 23 2018 *)

%o (PARI) x='x+O('x^27); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)/(1-x)^4) \\ _G. C. Greubel_, Jul 06 2018

%o (Magma) m:=27; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)/(1-x)^4)); // _G. C. Greubel_, Jul 06 2018

%K nonn,fini,full

%O 0,2

%A _N. J. A. Sloane_, Dec 02 2009