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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. - Milan Janjic, Aug 13 2010

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (4,3).

FORMULA

G.f.: (1-x)/(1-4*x-3*x^2).

a(n) = Sum_{k=0..n} 3^k*A122542(n,k).

Limit_{n->infinity} a(n+1)/a(n) = 2 + sqrt(7) = 4.645751311064....

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. - Paolo P. Lava, Nov 19 2008

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

PROG

(PARI) Vec((1-x)/(1-4*x-3*x^2) + O(x^30)) \\ Michel Marcus, Feb 04 2022

CROSSREFS

Cf. A122542.

Sequence in context: A217451 A213451 A224749 * A110211 A167874 A318967

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 October 6 21:32 EDT 2022. Contains 357270 sequences. (Running on oeis4.)