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A054894 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. 4
1, 2, 11, 48, 227, 1054, 4921, 22944, 107017, 499106, 2327795, 10856592, 50634107, 236152510, 1101392305, 5136786240, 23957470033, 111735303362, 521122556315, 2430464772336, 11335450631123, 52867436085214, 246568565219689, 1149971737922784, 5363356017597913, 25014169325118818 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Svenja Huntemann, Neil A. McKay, Counting Domineering Positions, arXiv:1909.12419 [math.CO], 2019.

Index entries for linear recurrences with constant coefficients, signature (4,4,-4,-1).

FORMULA

a(n) = Sum_{k=1..n} Fibonacci(k)^3*a(n-k), with a(0)=1. - Vladeta Jovovic, Apr 23 2003

G.f.: x*(1-2*x-x^2)/(1-4*x-4*x^2+4*x^3+x^4). - Vaclav Kotesovec, Nov 27 2012

MAPLE

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

MATHEMATICA

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 *)

LinearRecurrence[{4, 4, -4, -1}, {1, 2, 11, 48}, 40] (* Harvey P. Dale, May 28 2014 *)

PROG

(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

(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

(Sage)

def A054894_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

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

a=A054894_list(40); a[1:] # G. C. Greubel, Dec 29 2019

(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

CROSSREFS

Cf. A055518, A055519.

Sequence in context: A112288 A192699 A003442 * A270662 A330540 A139475

Adjacent sequences:  A054891 A054892 A054893 * A054895 A054896 A054897

KEYWORD

nonn,easy

AUTHOR

Barry Cipra, Jul 04 2000

STATUS

approved

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Last modified January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)