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%I #26 Sep 08 2022 08:45:58
%S 1,1,1,2,3,4,5,7,10,13,17,23,31,41,54,72,96,127,168,223,296,392,519,
%T 688,912,1208,1600,2120,2809,3721,4929,6530,8651,11460,15181,20111,
%U 26642,35293,46753,61935,82047,108689,143982,190736,252672,334719,443408,587391
%N Expansion of 1 / (1 - x - x^3 + x^6) in powers of x.
%H G. C. Greubel, <a href="/A193771/b193771.txt">Table of n, a(n) for n = 0..2500</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 0, 0, -1).
%F G.f.: 1 / (1 - x - x^3 + x^6) = 1 / (1 - x / (1 - x^2 / (1 + x^2 / (1 - x / (1 + x / (1 + x^2 / (1 - x^2))))))).
%F a(n) = a(n-1) + a(n-3) - a(n-6) for all n in Z.
%F Convolution of A008621 and A000931. PSUM transform of A017818.
%e G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 7*x^7 + 10*x^8 + 13*x^9 + ...
%t CoefficientList[Series[1/(1-x-x^3+x^6),{x,0,50}],x] (* or *) LinearRecurrence[ {1,0,1,0,0,-1},{1,1,1,2,3,4},50] (* _Harvey P. Dale_, Jul 25 2017 *)
%o (PARI) {a(n) = if( n<0, n = -n; polcoeff( - x^6 / (1 - x^3 - x^5 + x^6) + x * O(x^n), n), polcoeff( 1 / (1 - x - x^3 + x^6) + x * O(x^n), n))};
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^3+x^6))); // _G. C. Greubel_, Aug 10 2018
%Y Cf. A000931, A008621, A017818.
%K nonn
%O 0,4
%A _Michael Somos_, Jan 01 2013
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