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A147839 a(n)=9*a(n-1)-7*a(n-2), a(0)=1, a(1)=7 . 2
1, 7, 56, 455, 3703, 30142, 245357, 1997219, 16257472, 132336715, 1077228131, 8768696174, 71377668649, 581018144623, 4729519621064, 38498549577215, 313380308847487, 2550932932586878, 20764734231349493, 169026077554037291 (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 (9,-7).

FORMULA

a(n)=Sum_{k, 0<=k<=n}A147703(n,k)*6^k . G.f.: (1-2x)/(1-9x+7*x^2).

a(n)=-(5/106)*sqrt(53)*[(9/2)-(1/2)*sqrt(53)]^n+(5/106)*[(9/2)+(1/2)*sqrt(53)]^n*sqrt(53)+(1/2)*[(9 /2)+(1/2)*sqrt(53)]^n+(1/2)*[(9/2)-(1/2)*sqrt(53)]^n, with n>=0 [From Paolo P. Lava, Nov 18 2008]

a(n)= ((53+5*sqrt(53))/106)*(4.5+0.5*sqrt(53))^n + ((53-5*sqrt(53))/106)*(4.5-0.5*sqrt(53))^n [From Richard Choulet, Nov 20 2008]

MATHEMATICA

LinearRecurrence[{9, -7}, {1, 7}, 30] (* Harvey P. Dale, Nov 30 2019 *)

CROSSREFS

Sequence in context: A055274 A152776 A155197 * A126694 A305198 A264912

Adjacent sequences:  A147836 A147837 A147838 * A147840 A147841 A147842

KEYWORD

nonn

AUTHOR

Philippe Deléham, Nov 14 2008

STATUS

approved

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Last modified August 14 12:27 EDT 2020. Contains 336480 sequences. (Running on oeis4.)