A265107 Expansion of (2*x^4+x^3+x)/(-x^2-2*x+1).

0, 1, 2, 6, 16, 38, 92, 222, 536, 1294, 3124, 7542, 18208, 43958, 106124, 256206, 618536, 1493278, 3605092, 8703462, 21012016, 50727494, 122467004, 295661502, 713790008, 1723241518, 4160273044, 10043787606, 24247848256, 58539484118, 141326816492, 341193117102

Offset

0,3

Links

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

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

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

Formula

From Colin Barker, Apr 12 2016: (Start)

a(n) = ((1+sqrt(2))^n*(-5+4*sqrt(2)) + (1-sqrt(2))^n*(5+4*sqrt(2)))/sqrt(2) for n>2.

a(n) = 2*a(n-1)+a(n-2) for n>4.

(End)

Mathematica

Join[{0, 1, 2}, LinearRecurrence[{2, 1}, {6, 16}, 30]] (* Jean-François Alcover, Nov 02 2021 *)

Prog

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

Crossrefs

Cf. A002605, A265106, A265278, A270810.

Sequence in context: A156616 A330886 A265758 * A217631 A046209 A285885

Adjacent sequences: A265104 A265105 A265106 * A265108 A265109 A265110

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 06 2016

Status

approved