|
| |
|
|
A147518
|
|
Expansion of (1-x)/(1-4*x-6*x^2).
|
|
1
| |
|
|
1, 3, 18, 90, 468, 2412, 12456, 64296, 331920, 1713456, 8845344, 45662112, 235720512, 1216854720, 6281741952, 32428096128, 167402836224, 864179921664, 4461136704000, 23029626345984, 118885325607936, 613719060507648
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Binomial transform of [1,2,13,44,205,...] = A002534(n+1).
a(n) is the number of compositions of n when there are 3 types of 1 and 9 types of other natural numbers. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
|
|
|
FORMULA
| a(n)=4*a(n-1)+6*a(n-2); a(0)=1, a(1)=3. a(n)=Sum_{k, 0<=k<=n}A122016(n,k)*3^k.
a(n)=(1/2)*[2+sqrt(10)]^n-(1/20)*[2-sqrt(10)]^n*sqrt(10)+(1/20)*[2+sqrt(10)]^n*sqrt(10)+(1/2) *[2-sqrt(10)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 18 2008]
a(n)= ((10+sqrt(10))/20)*(2+sqrt(10))^n+((10-sqrt(10))/20)*(2-sqrt(10))^n [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 20 2008]
|
|
|
CROSSREFS
| Cf. A026150, A122117
Sequence in context: A037295 A124811 A006568 * A088336 A133594 A092691
Adjacent sequences: A147515 A147516 A147517 * A147519 A147520 A147521
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 06 2008
|
| |
|
|
