|
| |
|
|
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; 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 R. Janjic (agnus(AT)blic.net), Aug 13 2010]
|
|
|
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 (paoloplava(AT)gmail.com), Nov 19 2008]
a(n)= ((7+sqrt(7))/14)*(2+sqrt(7))^n+ ((7-sqrt(7))/14)*(2-sqrt(7))^n [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 20 2008]
|
|
|
CROSSREFS
| Sequence in context: A106732 A052981 A086200 * A110211 A167874 A033876
Adjacent sequences: A122555 A122556 A122557 * A122559 A122560 A122561
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006, Sep 22 2006
|
|
|
EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
|
| |
|
|
