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

Author

Clark Kimberling

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A001075.

Programs

PARI

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

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