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