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A154996 a(n)=5*a(n-1)+20*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=9 . 2
1, 1, 9, 65, 505, 3825, 29225, 222625, 1697625, 12940625, 98655625, 752090625, 5733565625, 43709640625, 333219515625, 2540290390625, 19365842265625, 147635019140625, 1125491941015625, 8580160087890625, 65410639259765625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (5, 20).

FORMULA

G.f.: (1-4*x-16*x^2)/(1-5*x-20*x^2) . a(n+1)=Sum_{k, 0<=k<=n}A154929(n,k)*4^(n-k).

a(n)=(1/2)*{[(5/2)-(1/2)*sqrt(105)]^(n-1)+[(5/2)+(1/2)*sqrt(105)]^(n-1)}+(13/210)*sqrt(105)*{[(5/2)+(1/2)*sqrt(105)]^(n-1)-[(5/2)-(1/2)*sqrt(105)]^(n-1)}+(4/5)*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Jan 20 2009]

MATHEMATICA

Join[{1}, LinearRecurrence[{5, 20}, {1, 9}, 20]] (* Harvey P. Dale, Jan 19 2012 *)

CROSSREFS

Sequence in context: A287816 A036731 A020234 * A128195 A103459 A100311

Adjacent sequences:  A154993 A154994 A154995 * A154997 A154998 A154999

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jan 18 2009

STATUS

approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)