|
| |
|
|
A099621
|
|
Sum C(n-k,k+1)3^(n-k-1)(4/3)^k, k=0..floor(n/2).
|
|
1
| |
|
|
0, 1, 6, 31, 144, 637, 2730, 11467, 47508, 194953, 794574, 3222583, 13023192, 52491349, 211161138, 848231779, 3403688796, 13647040225, 54685016022, 219030629455, 876994213920, 3510591943981, 14050213040826, 56224387958011
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| In general a(n)=sum{k=0..floor(n/2),C(n-k,k+1)u^(n-k-1)(v/u)^(k-1)} has g.f. x^2/((1-u*x)(1-u*x-v*x^2)) and satisfies the recurrence a(n)=2u*a(n-1)-(u^2-v)a(n-2)-u*v*a(n-3).
|
|
|
FORMULA
| G.f.: x^2/((1-3x)(1-3x-4x^2)); a(n)=6a(n-1)-5a(n-2)-12a(n-3).
|
|
|
CROSSREFS
| Cf. A094705, A099622.
Sequence in context: A009076 A012714 A094951 * A056015 A128740 A026705
Adjacent sequences: A099618 A099619 A099620 * A099622 A099623 A099624
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 25 2004
|
| |
|
|
