A155197 a(n) = 8*a(n-1) + a(n-2) for n>2, with a(0)=1, a(1)=7, a(2)=56.

1, 7, 56, 455, 3696, 30023, 243880, 1981063, 16092384, 130720135, 1061853464, 8625547847, 70066236240, 569155437767, 4623309738376, 37555633344775, 305068376496576, 2478102645317383, 20129889539035640, 163517218957602503

Offset: 0

Author

Philippe Deléham, Jan 21 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (8,1).

Crossrefs

Cf. A155161.

Programs

Maple

a:=proc(n) option remember; if n=0 then 1 elif n=1 then 7 elif n=2 then 56 else 8*a(n-1)+a(n-2); fi; end: seq(a(n), n=0..30); # Wesley Ivan Hurt, Jan 28 2017

Mathematica

LinearRecurrence[{8, 1}, {1, 7, 56}, 20] (* or *)
CoefficientList[Series[(1 - x - x^2)/(1 - 8 x - x^2), {x, 0, 19}], x] (* or *)
{1, 7}~Join~Table[Simplify[# (14/17) ((4 + #)^n - (4 - #)^n) + (7/2) ((4 + #)^n + (4 - #)^n) + Mod[Binomial[2 n, n], 2]] &@ Sqrt@ 17, {n, 18}] (* Michael De Vlieger, Jan 30 2017 *)

Formula

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

a(n) = Sum_{k=0..n} A155161(n,k)*7^k. - Philippe Deléham, Feb 08 2012