%I #36 Sep 08 2022 08:45:01

%S 1,2,11,48,227,1054,4921,22944,107017,499106,2327795,10856592,

%T 50634107,236152510,1101392305,5136786240,23957470033,111735303362,

%U 521122556315,2430464772336,11335450631123,52867436085214,246568565219689,1149971737922784,5363356017597913,25014169325118818

%N a(n+1) = 4*a(n) + 4*a(n-1) - 4*a(n-2) - a(n-3) with a(1)=1, a(2)=2, a(3)=11, a(4)=48.

%H Vincenzo Librandi, <a href="/A054894/b054894.txt">Table of n, a(n) for n = 1..1000</a>

%H Svenja Huntemann, Neil A. McKay, <a href="https://arxiv.org/abs/1909.12419">Counting Domineering Positions</a>, arXiv:1909.12419 [math.CO], 2019.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,-4,-1).

%F a(n) = Sum_{k=1..n} Fibonacci(k)^3*a(n-k), with a(0)=1. - _Vladeta Jovovic_, Apr 23 2003

%F G.f.: x*(1-2*x-x^2)/(1-4*x-4*x^2+4*x^3+x^4). - _Vaclav Kotesovec_, Nov 27 2012

%p seq(coeff(series(x^4/((1+2*x)*(2*x^3+x^2-2*x+1)), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Dec 29 2019

%t CoefficientList[Series[(1-2*x-x^2)/(1-4*x-4*x^2+4*x^3+x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 05 2013 *)

%t LinearRecurrence[{4,4,-4,-1},{1,2,11,48},40] (* _Harvey P. Dale_, May 28 2014 *)

%o (PARI) my(x='x+O('x^66)); Vec(x*(1-2*x-x^2)/(1-4*x-4*x^2+4*x^3+x^4)) \\ _Joerg Arndt_, May 06 2013

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1-2*x-x^2)/(1-4*x-4*x^2+4*x^3+x^4) )); // _G. C. Greubel_, Dec 29 2019

%o (Sage)

%o def A054894_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( x*(1-2*x-x^2)/(1-4*x-4*x^2+4*x^3+x^4) ).list()

%o a=A054894_list(40); a[1:] # _G. C. Greubel_, Dec 29 2019

%o (GAP) a:=[1,2,11,48];; for n in [5..40] do a[n]:=4*(a[n-1]+a[n-2]-a[n-3]) -a[n-4]; od; a; # _G. C. Greubel_, Dec 29 2019

%Y Column 3 of A332862 (apart from the initial term 1 here).

%Y Cf. A055518, A055519.

%K nonn,easy

%O 1,2

%A _Barry Cipra_, Jul 04 2000