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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

%I

%S 1,3,15,69,321,1491,6927,32181,149505,694563,3226767,14990757,

%T 69643329,323545587,1503112335,6983086101,32441681409,150715983939,

%U 700188979983,3252903871749,15112182426945,70207441323027,326166312572943

%N a(0)=1, a(1)=3, a(n)=4*a(n-1)+3*a(n-2) for n>1.

%C 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]

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

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

%F 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]

%F a(n)= ((7+sqrt(7))/14)*(2+sqrt(7))^n+ ((7-sqrt(7))/14)*(2-sqrt(7))^n [From _Richard Choulet_, Nov 20 2008]

%K nonn

%O 0,2

%A _Philippe Deléham_, Sep 20 2006, Sep 22 2006

%E Corrected by _T. D. Noe_, Nov 07 2006

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Last modified March 3 03:03 EST 2021. Contains 341756 sequences. (Running on oeis4.)