A271944 Expansion of 2*x*(1 + x)/(1 - x - 9*x^2 + x^3).

0, 2, 4, 22, 56, 250, 732, 2926, 9264, 34866, 115316, 419846, 1422824, 5086122, 17471692, 61823966, 213983072, 752927074, 2616950756, 9179311350, 31978941080, 111975792474, 390606950844, 1366410142030, 4769896907152, 16676981234578, 58239643256916

Offset: 0

Author

Vincenzo Librandi, Apr 18 2016

Keywords

• nonn
• easy

Links

• Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3 (p. 26, table 5).
• Index entries for linear recurrences with constant coefficients, signature (1,9,-1).

Crossrefs

Cf. A121442.

Programs

Magma

[n le 2 select 2*n else Self(n)+9*Self(n-1)-Self(n-2): n in [0..30]];

Mathematica

CoefficientList[Series[2 x (1 + x)/(1 - x - 9 x^2 + x^3), {x, 0, 33}], x]

PARI

x='x+O('x^99); concat(0, Vec(2*x*(1+x)/(1-x-9*x^2+x^3))) \\ Altug Alkan, Apr 18 2016

Sage

gf = 2*x*(1+x)/(1-x-9*x^2+x^3); taylor(gf, x, 0, 40).list() # Bruno Berselli, Apr 18 2016

Formula

G.f.: 2*x*(1 + x)/(1 - x - 9*x^2 + x^3).

a(n) = a(n-1) + 9*a(n-2) - a(n-3).