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A265107
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Expansion of (2*x^4+x^3+x)/(-x^2-2*x+1).
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5
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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
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OFFSET
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0,3
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LINKS
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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).
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FORMULA
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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)
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MATHEMATICA
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Join[{0, 1, 2}, LinearRecurrence[{2, 1}, {6, 16}, 30]] (* Jean-François Alcover, Nov 02 2021 *)
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PROG
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(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
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CROSSREFS
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Cf. A002605, A265106, A265278, A270810.
Sequence in context: A156616 A330886 A265758 * A217631 A046209 A285885
Adjacent sequences: A265104 A265105 A265106 * A265108 A265109 A265110
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KEYWORD
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nonn,easy
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AUTHOR
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Alois P. Heinz, Apr 06 2016
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STATUS
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approved
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