|
| |
|
|
A091147
|
|
Expansion of (1-x-sqrt(1-2x-15x^2))/(8x^2).
|
|
0
| |
|
|
1, 1, 5, 13, 57, 201, 861, 3445, 14897, 63313, 278389, 1223069, 5465065, 24513945, 111037005, 505298565, 2314343265, 10645982625, 49202944485, 228253816365, 1062783893145, 4964167491945, 23256852644925, 109249893866133
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| a(n)=A014433(n+1)/4
Number of lattice paths in the first quadrant from (0,0) to (n,0) using only steps H=(1,0), U=(1,1) and D=(1,-1), where the U steps come in 4 colors (i.e. Motzkin paths with the up steps in 4 colors). Series reversion of x/(1+x+4x^2). - Paul Barry (pbarry(AT)wit.ie), May 16 2005
|
|
|
FORMULA
| G.f.: 2/(1-x+sqrt(1-2x-15x^2)); a(n)=sum{k=0..n, binomial(n, k)4^(k/2)C(k/2)(1+(-1)^k)/2}, C(n)=A000108(n).
a(n)=sum{k=0..n, C(n, 2k)C(k)4^k}; - Paul Barry (pbarry(AT)wit.ie), May 16 2005
a(n) = integral(x=-2..2, (2*x+1)^n*sqrt((2-x)*(2+x)))/(2*Pi). [Peter Luschny, Sep 11 2011]
|
|
|
CROSSREFS
| Sequence in context: A149551 A149552 A084136 * A149553 A149554 A149555
Adjacent sequences: A091144 A091145 A091146 * A091148 A091149 A091150
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Dec 22 2003
|
| |
|
|
