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A122558 a(0)=1, a(1)=3, a(n)=4*a(n-1)+3*a(n-2) for n>1. 2
1, 3, 15, 69, 321, 1491, 6927, 32181, 149505, 694563, 3226767, 14990757, 69643329, 323545587, 1503112335, 6983086101, 32441681409, 150715983939, 700188979983, 3252903871749, 15112182426945, 70207441323027, 326166312572943 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of compositions of n when there are 3 types of 1 and 6 types of other natural numbers. [From Milan Janjic, Aug 13 2010]

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f. (1-x)/(1-4*x-3*x^2) . a(n)=Sum_{k, 0<=k<=n} 3^k*A122542(n,k).

a(n+1)/a(n)-> 2+sqrt(7)= 4,645751311064... if n->infinity.

a(n)=-(1/14)*[2-sqrt(7)]^n*sqrt(7)+(1/14)*sqrt(7)*[2+sqrt(7)]^n+(1/2)*[2-sqrt(7)]^n+(1/2)*[2 +sqrt(7)]^n [From Paolo P. Lava, Nov 19 2008]

a(n)= ((7+sqrt(7))/14)*(2+sqrt(7))^n+ ((7-sqrt(7))/14)*(2-sqrt(7))^n [From Richard Choulet, Nov 20 2008]

CROSSREFS

Sequence in context: A217451 A213451 A224749 * A110211 A167874 A277370

Adjacent sequences:  A122555 A122556 A122557 * A122559 A122560 A122561

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 20 2006, Sep 22 2006

EXTENSIONS

Corrected by T. D. Noe, Nov 07 2006

STATUS

approved

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Last modified September 25 21:33 EDT 2017. Contains 292500 sequences.