A133469 a(n) = a(n-1) + 7*a(n-2) for n >= 2, a(0)=1, a(1)=2.

1, 2, 9, 23, 86, 247, 849, 2578, 8521, 26567, 86214, 272183, 875681, 2780962, 8910729, 28377463, 90752566, 289394807, 924662769, 2950426418, 9423065801, 30076050727, 96037511334, 306569866423, 978832445761, 3124821510722

Offset: 0

Author

Philippe Deléham, Jan 03 2008

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..1981
• Index entries for linear recurrences with constant coefficients, signature (1, 7).

Programs

Maple

f:= gfun:-rectoproc({a(n) = a(n-1) + 7*a(n-2), a(0)=1, a(1)=2}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Jul 23 2017

Mathematica

LinearRecurrence[{1,7},{1,2},30] (* Harvey P. Dale, Dec 09 2013 *)

PARI

x='x+O('x^99); Vec((1+x)/(1-x-7*x^2)) \\ Altug Alkan, Jul 23 2017

Formula

G.f.: (1+x)/(1-x-7*x^2) .

a(n) = Sum_{k=0..n+1} A122950(n+1,k)*6^(n+1-k). - Philippe Deléham, Jan 08 2008

a(n) = ((29 + 3*sqrt(29))/58)*(0.5 + 0.5*sqrt(29))^n + ((29 - 3*sqrt(29))/58)*(0.5 - 0.5*sqrt(29))^n. - Richard Choulet, Nov 20 2008