|
%I #38 Dec 16 2023 16:59:40
%S 1,7,56,455,3696,30023,243880,1981063,16092384,130720135,1061853464,
%T 8625547847,70066236240,569155437767,4623309738376,37555633344775,
%U 305068376496576,2478102645317383,20129889539035640,163517218957602503
%N a(n) = 8*a(n-1) + a(n-2) for n>2, with a(0)=1, a(1)=7, a(2)=56.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,1).
%F G.f.: (1-x-x^2)/(1-8*x-x^2).
%F a(n) = Sum_{k=0..n} A155161(n,k)*7^k. - _Philippe Deléham_, Feb 08 2012
%p 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
%t LinearRecurrence[{8, 1}, {1, 7, 56}, 20] (* or *)
%t CoefficientList[Series[(1 - x - x^2)/(1 - 8 x - x^2), {x, 0, 19}], x] (* or *)
%t {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 *)
%Y Cf. A155161.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 21 2009
|
