|
Search: id:A084609
|
|
|
| A084609 |
|
Coefficients of 1/(1-4x-8x^2)^(1/2); also, a(n) is the central coefficient of (1+2x+3x^2)^n. |
|
+0
8
|
|
| 1, 2, 10, 44, 214, 1052, 5284, 26840, 137638, 710828, 3692140, 19266920, 100932220, 530479640, 2795917960, 14771797424, 78210099718, 414862155980, 2204273582236, 11729283976136, 62496686731924, 333400654676168
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), U can have 3 colors and H can have 2 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
|
|
REFERENCES
|
Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
|
|
FORMULA
|
a(n)=sum{k=0..floor(n/2), Binomial(n, k)Binomial(2(n-k), n)2^k} - Paul Barry (pbarry(AT)wit.ie), Sep 08 2004
a(n)=sum{k=0..floor(n/2), C(n,2k)*C(2k,k)*3^k*2^(n-2k)}; a(n)=sum{k=0..floor(n/2), C(n,k)*C(n-k,k)*3^k*2^(n-2k)}. - Paul Barry (pbarry(AT)wit.ie), Sep 19 2006
|
|
PROGRAM
|
(PARI) for(n=0, 30, t=polcoeff((1+2*x+3*x^2)^n, n, x); print1(t", "))
|
|
CROSSREFS
|
Cf. A002426, A084600-A084608, A084610-A084615.
Sequence in context: A099919 A100397 A084059 this_sequence A105485 A151313 A144896
Adjacent sequences: A084606 A084607 A084608 this_sequence A084610 A084611 A084612
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jun 01 2003
|
|
|
Search completed in 0.002 seconds
|
