cp's OEIS Frontend

A192910 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.

%I A192910 #15 Sep 08 2022 08:45:58
%S A192910 0,1,4,13,42,133,418,1311,4110,12883,40380,126563,396684,1243317,
%T A192910 3896896,12213937,38281814,119985657,376067806,1178699171,3694364986,
%U A192910 11579148423,36292212248,113749700903,356522616120,1117439209033,3502359540252
%N A192910 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
%C A192910 The titular polynomial is defined by p(n,x) = (x^2)*p(n-1,x) + x*p(n-2,x) + 1, with p(0,x) = 1, p(1,x) = x + 1.
%H A192910 G. C. Greubel, <a href="/A192910/b192910.txt">Table of n, a(n) for n = 0..1000</a>
%H A192910 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,1,0,-1).
%F A192910 a(n) = 4*a(n-1) - 3*a(n-2) + a(n-3) - a(n-5).
%F A192910 G.f.: x*(1+x)*(1-x+x^2)/((1-x)*(1-3*x-x^3-x^4)). - _R. J. Mathar_, Jul 13 2011
%t A192910 (See A192909.)
%t A192910 LinearRecurrence[{4,-3,1,0,-1}, {0,1,4,13,42}, 30] (* _G. C. Greubel_, Jan 12 2019 *)
%o A192910 (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1+x)*(1-x+x^2)/((1-x)*(1-3*x -x^3-x^4)))) \\ _G. C. Greubel_, Jan 12 2019
%o A192910 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1+x)*(1-x+x^2)/((1-x)*(1-3*x-x^3-x^4)) )); // _G. C. Greubel_, Jan 12 2019
%o A192910 (Sage) (x*(1+x)*(1-x+x^2)/((1-x)*(1-3*x-x^3-x^4))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jan 12 2019
%o A192910 (GAP) a:=[0,1,4,13,42];; for n in [6..30] do a[n]:=4*a[n-1]-3*a[n-2] + a[n-3]-a[n-5]; od; a; # _G. C. Greubel_, Jan 12 2019
%Y A192910 Cf. A192232, A192744, A192872, A192904, A192909.
%K A192910 nonn
%O A192910 0,3
%A A192910 _Clark Kimberling_, Jul 12 2011