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A015583 a(0) = 0, a(1) = 1; for n >= 2, a(n) = 9*a(n-1) + 7*a(n-2). 3
0, 1, 9, 88, 855, 8311, 80784, 785233, 7632585, 74189896, 721137159, 7009563703, 68134033440, 662273246881, 6437397456009, 62572489832248, 608214190682295, 5911935144966391, 57464915639473584, 558567786770026993, 5429364490406558025, 52774254921049211176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,7).

FORMULA

G.f.: 1/(1 - 9*x - 7*x^2). - Zerinvary Lajos, Dec 20 2008

a(n) = (1/109)*sqrt(109)*(((9+sqrt(109))/2)^n - ((9-sqrt(109))/2)^n), with n >= 0. - Paolo P. Lava, Jan 13 2009

MAPLE

a:=proc(n) option remember: if n=0 then 0 elif n=1 then 1 else 9*procname(n-1)+7*procname(n-2) fi: end; seq(a(n), n=0..22); # Muniru A Asiru, Jul 15 2018

MATHEMATICA

Join[{a=0, b=1}, Table[c=9*b+7*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)

LinearRecurrence[{9, 7}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)

PROG

(Sage) [lucas_number1(n, 9, -7) for n in xrange(0, 19)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) [n le 2 select n-1 else 9*Self(n-1) + 7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

(PARI) x='x+O('x^30); concat([0], Vec(1/(1-9*x-7*x^2))) \\ G. C. Greubel, Jan 06 2018

(GAP) a:=[0, 1];; for n in [3..22] do a[n]:=9*a[n-1]+7*a[n-2]; od; a; # Muniru A Asiru, Jul 15 2018

CROSSREFS

Cf. A015579, A099371.

Sequence in context: A035101 A245491 A160466 * A152266 A260041 A084022

Adjacent sequences:  A015580 A015581 A015582 * A015584 A015585 A015586

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Extended by T. D. Noe, May 23 2011

STATUS

approved

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Last modified December 6 19:22 EST 2019. Contains 329809 sequences. (Running on oeis4.)