A115109 Expansion of (1 -2*x +4*x^2 -22*x^3 +6*x^4 +268*x^5 -854*x^6 +3596*x^7 -3100*x^8)/((1 -2*x)/(1 -2*x -4*x^2)).

1, 2, 12, 18, 62, 420, 682, 5828, 16852, 61952, 201184, 669920, 2184064, 7126784, 23147776, 75118592, 243460096, 788658176, 2553683968, 8267055104, 26758955008, 86606348288, 280288952320, 907084169216, 2935485890560

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (4,0,-8).

Formula

G.f.: -(3100*x^8 -3596*x^7 +854*x^6 -268*x^5 -6*x^4 +22*x^3 -4*x^2 +2*x -1) / ((2*x -1)*(4*x^2 +2*x -1)). - Colin Barker, Mar 15 2013

a(n) = +4*a(n-1) -8*a(n-3). - Colin Barker, Mar 15 2013

Mathematica

Join[{1, 2, 12, 18, 62, 420}, {LinearRecurrence[{4, 0, -8}, {682, 5828, 16852}, 20]}] (* Bruno Berselli, Mar 15 2013 *)

Prog

(Magma) I:=[1, 2, 12, 18, 62, 420, 682, 5828, 16852]; [n le 9 select I[n] else 4*Self(n-1) - 8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Mar 18 2013

Crossrefs

Sequence in context: A190044 A066238 A101074 * A048001 A109299 A216629

Adjacent sequences: A115106 A115107 A115108 * A115110 A115111 A115112

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 03 2006

Extensions

Definition rewritten using Colin Barker's g.f. by Bruno Berselli, Mar 15 2013

Status

approved