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

Monica Anderson, Marika Diepenbroek, Lara Pudwell, and Alex Stoll, Pattern Avoidance in Reverse Double Lists, Discrete Mathematics and Theoretical Computer Science, Vol. 19, No. 2 (2018), Article #14. 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)

a(n) = A002203(n-2) + 2*A000129(n-1) for n >= 3. - Amiram Eldar, Jan 10 2026

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. A000129, A002203, 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