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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved