A265106 Expansion of (x^5-x^4-2*x^3+x^2-x)/(-x^4+x^3-2*x^2+3*x-1).

0, 1, 2, 6, 16, 36, 80, 178, 394, 870, 1920, 4236, 9344, 20610, 45458, 100262, 221136, 487732, 1075728, 2372594, 5232922, 11541574, 25455744, 56144412, 123830400, 273116546, 602377506, 1328585414, 2930287376, 6462952260, 14254489936, 31439267250, 69341486762

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

M. Diepenbroek, M. Maus, A. Stoll, Pattern Avoidance in Reverse Double Lists, Preprint 2015. See Table 3.

Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-1).

Formula

a(n) = 3*a(n-1)-2*a(n-2)+a(n-3)-a(n-4) for n>5. - Colin Barker, Apr 12 2016

a(n) = 2*a(n-1) + a(n-3) + 2 for n>4. - Greg Dresden, Feb 09 2020

Mathematica

CoefficientList[Series[(x^5-x^4-2x^3+x^2-x)/(-x^4+x^3-2x^2+3x-1), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, -2, 1, -1}, {0, 1, 2, 6, 16, 36}, 40] (* Harvey P. Dale, Feb 05 2019 *)

Prog

(PARI) concat(0, Vec(x*(1-x+2*x^2+x^3-x^4)/((1-x)*(1-2*x-x^3)) + O(x^50))) \\ Colin Barker, Apr 12 2016

Crossrefs

Cf. A002605, A265107, A265278, A270810.

Sequence in context: A257198 A053210 A066641 * A306332 A331393 A026540

Adjacent sequences: A265103 A265104 A265105 * A265107 A265108 A265109

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 06 2016

Status

approved