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A165311 a(0)=1, a(1)=4, a(n)=9*a(n-1)-16*a(n-2) for n>1. 2
1, 4, 20, 116, 724, 4660, 30356, 198644, 1302100, 8540596, 56031764, 367636340, 2412218836, 15827788084, 103854591380, 681446713076, 4471346955604, 29338975191220, 192509225431316, 1263159425822324, 8288287225499860 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/a(n-1) tends to (9+sqrt(17))/2 = 6.56155281...

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9,-16).

FORMULA

G.f.: (1-5x)/(1-9x+16x^2). a(n)=Sum_{k, 0<=k<=n}A165253(n,k)*4^(n-k).

a(n) = ((17-sqrt(17))*(9+sqrt(17))^n+(17+sqrt(17))*(9-sqrt(17))^n )/(34*2^n). [From Klaus Brockhaus, Sep 26 2009]

MATHEMATICA

LinearRecurrence[{9, -16}, {1, 4}, 30] (* Harvey P. Dale, Feb 19 2015 *)

CROSSREFS

Sequence in context: A085458 A085456 A120915 * A100328 A082298 A129378

Adjacent sequences:  A165308 A165309 A165310 * A165312 A165313 A165314

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 14 2009

STATUS

approved

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Last modified September 23 12:11 EDT 2021. Contains 347617 sequences. (Running on oeis4.)