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A155197 a(n) = 8*a(n-1) + a(n-2) for n>2, with a(0)=1, a(1)=7, a(2)=56. 1
1, 7, 56, 455, 3696, 30023, 243880, 1981063, 16092384, 130720135, 1061853464, 8625547847, 70066236240, 569155437767, 4623309738376, 37555633344775, 305068376496576, 2478102645317383, 20129889539035640, 163517218957602503 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

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

FORMULA

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

a(n) = (14/17)*sqrt(17)*((4+sqrt(17))^(n-1) - (4-sqrt(17))^(n-1)) + (7/2)*((4+sqrt(17))^(n-1) + (4-sqrt(17))^(n-1)) for n>0, a(0)=1. - Paolo P. Lava, Jan 26 2009

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

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 *)

CROSSREFS

Cf. A155161.

Sequence in context: A156362 A055274 A152776 * A147839 A126694 A305198

Adjacent sequences: A155194 A155195 A155196 * A155198 A155199 A155200

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Jan 21 2009

STATUS

approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)