A026030 a(n) = T(2n,n-1), where T is defined in A026022.

1, 4, 15, 56, 209, 780, 2912, 10880, 40698, 152456, 572033, 2150040, 8095425, 30535260, 115377660, 436698240, 1655607390, 6286707000, 23908446510, 91057063344, 347281885818, 1326262602104, 5071418015120, 19415851639296, 74419447792340

Offset

1,2

Comments

a(n) = number of (s(0), s(1), ..., s(2n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 3, s(2n) = 5.

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = C(2n, n-1) - C(2n, n-5). G.f.: (1+x^2C^4)*C^4, where C=(1-sqrt(1-4x))/(2x). - Ralf Stephan, Jan 09 2005

G.f.: 2*x*(1-2*x) / ((1-2*x)*(1-4*x+x^2) + (1-x)*(1-3*x)*sqrt(1-4*x)). - Michael Somos, Jan 08 2012

Conjecture: (n+5)*a(n) -2*(5*n+16)*a(n-1) +(35*n+47)*a(n-2) +2*(-25*n+14)*a(n-3) +12*(2*n-5)*a(n-4)=0. - R. J. Mathar, Jun 15 2014

Example

x + 4*x^2 + 15*x^3 + 56*x^4 + 209*x^5 + 780*x^6 + 2912*x^7 + 10880*x^8 + ...

Prog

(PARI) {a(n) = binomial( 2*n, n-1) - binomial( 2*n, n-5)} /* Michael Somos, Jan 08 2012 */

Crossrefs

Cf. A001075.

Sequence in context: A195503 A001353 A010905 * A047038 A158500 A001791

Adjacent sequences: A026027 A026028 A026029 * A026031 A026032 A026033

Keyword

nonn

Author

Clark Kimberling

Status

approved