A190943 a(n) = 8*a(n-1) + 27*a(n-2), with a(0)=0, a(1)=1.

0, 1, 8, 91, 944, 10009, 105560, 1114723, 11767904, 124240753, 1311659432, 13847775787, 146197010960, 1543466033929, 16295047567352, 172033963454899, 1816237991957696, 19174820948943841, 202436993374408520, 2137216112616751867

Offset

0,3

Links

Bruno Berselli, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (8, 27).

Formula

G.f.: x/(1-8*x-27*x^2).

a(n) = ((4+sqrt(43))^n - (4-sqrt(43))^n)/(2*sqrt(43)).

Mathematica

a = {0, 1}; Do[AppendTo[a, 8 a[[-1]] + 27 a[[-2]]], {18}]; a (* Bruno Berselli, Dec 26 2012 *)
CoefficientList[Series[x / (1 - 8 x - 27 x^2), {x, 0, 25}], x] (* Vincenzo Librandi, Aug 19 2013 *)

Prog

(Maxima) a[0]:0$ a[1]:1$ a[n]:=8*a[n-1]+27*a[n-2]$ makelist(a[n], n, 0, 17);
(Magma) [n le 2 select n-1 else 8*Self(n-1)+27*Self(n-2): n in [1..17]];
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-8*x-27*x^2))) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A000045, A046717, A015533 (for type of recurrence).

Cf. A015611, A190441 (for type of closed formula).

Sequence in context: A034667 A116149 A184709 * A180912 A234280 A298013

Adjacent sequences: A190940 A190941 A190942 * A190944 A190945 A190946

Keyword

nonn,easy

Author

Bruno Berselli, May 24 2011

Status

approved