%I #25 Sep 08 2022 08:46:06

%S 1,1,1,1,2,3,4,5,7,9,12,16,22,29,38,50,67,89,118,156,207,274,363,481,

%T 638,845,1119,1482,1964,2602,3447,4566,6049,8013,10615,14062,18629,

%U 24678,32691,43306,57369,75998,100676,133367,176674,234043,310041,410717

%N Expansion of 1 / (1 - x - x^4 + x^9) in powers of x.

%H G. C. Greubel, <a href="/A233522/b233522.txt">Table of n, a(n) for n = 0..2500</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,0,0,0,0,-1).

%F a(n) = a(n-1) + a(n-4) - a(n-9) for all n in Z.

%F a(n) - a(n-1) = A017830(n).

%F G.f.: 1 / ((1 - x) * (1 + x) * (1 + x^2) * (1 - x - x^5)).

%e G.f. = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + ...

%t a[ n_] := SeriesCoefficient[ If[ n >= 0, 1 / (1 - x - x^4 + x^9), -x^9 / (1 - x^5 - x^8 + x^9)], {x, 0, Abs@n}];

%o (PARI) {a(n) = if( n>=0, polcoeff( 1 / (1 - x - x^4 + x^9) + x * O(x^n), n), polcoeff( -x^9 / (1 - x^5 - x^8 + x^9) + x * O(x^-n), -n))};

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/( 1-x-x^4+x^9))); // _G. C. Greubel_, Aug 08 2018

%Y Cf. A017830.

%K nonn,easy

%O 0,5

%A _Michael Somos_, Dec 11 2013