A026031 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) = 7. Also a(n) = T(2n,n-2), where T is defined in A026022.

1, 6, 28, 120, 494, 1988, 7888, 31008, 121125, 471086, 1826660, 7068360, 27313650, 105452700, 406923360, 1569869760, 6056194410, 23366193084, 90173331960, 348102883184, 1344324544156, 5193831553416, 20075820280544, 77637309982400

Offset

2,2

Links

Table of n, a(n) for n=2..25.

Formula

C(2n, n-2) - C(2n, n-6). G.f.: (1+x^2C^4)*C^6, where C=(1-sqrt(1-4x))/(2x). - Ralf Stephan, Jan 09 2005

Conjecture: (n+6)*a(n) +10*(-n-4)*a(n-1) +2*(17*n+32)*a(n-2) +4*(-11*n+4)*a(n-3) +8*(2*n-5)*a(n-4)=0. - R. J. Mathar, Jun 22 2013

Mathematica

Table[Binomial[2n, n-2]-Binomial[2n, n-6], {n, 2, 30}] (* Harvey P. Dale, May 28 2017 *)

Crossrefs

Sequence in context: A055717 A090777 A055715 * A002694 A342924 A007691

Adjacent sequences: A026028 A026029 A026030 * A026032 A026033 A026034

Keyword

nonn

Author

Clark Kimberling

Status

approved