OFFSET
0,3
LINKS
Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3 (page 26, table 5).
Index entries for linear recurrences with constant coefficients, signature (1,9,-1).
FORMULA
G.f.: 4*x^2/(1 - x - 9*x^2 + x^3).
a(n) = a(n-1) + 9*a(n-2) - a(n-3).
MATHEMATICA
CoefficientList[Series[4 x^2 /(1 - x - 9 x^2 + x^3), {x, 0, 30}], x]
LinearRecurrence[{1, 9, -1}, {0, 0, 4}, 30] (* Harvey P. Dale, Jul 18 2021 *)
PROG
(Magma) [n le 2 select 2*n*(n-1) else Self(n)+9*Self(n-1)-Self(n-2): n in [0..30]];
(PARI) x='x+O('x^99); concat([0, 0], Vec(4*x^2/(1-x-9*x^2+x^3))) \\ Altug Alkan, Apr 18 2016
(Sage) gf = 4*x^2/(1 - x - 9*x^2 + x^3); taylor(gf, x, 0, 30).list() # Bruno Berselli, Apr 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 18 2016
STATUS
approved