A015583 a(0) = 0, a(1) = 1; for n >= 2, a(n) = 9*a(n-1) + 7*a(n-2).

0, 1, 9, 88, 855, 8311, 80784, 785233, 7632585, 74189896, 721137159, 7009563703, 68134033440, 662273246881, 6437397456009, 62572489832248, 608214190682295, 5911935144966391, 57464915639473584, 558567786770026993, 5429364490406558025, 52774254921049211176

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,7).

Crossrefs

Cf. A015579, A099371.

Programs

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

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

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 *)

PARI

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

Sage

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

Formula

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

Extensions

Extended by T. D. Noe, May 23 2011