A026027 a(n) = number of (s(0), s(1), ..., s(2*n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 3, s(2*n-1) = 6. Also a(n) = T(2*n-1,n-2), where T is defined in A026022.

1, 5, 21, 84, 329, 1274, 4900, 18768, 71706, 273581, 1043119, 3976700, 15163785, 57848910, 220830360, 843621600, 3225477150, 12342901410, 47274639594, 181230395304, 695384769002, 2670587146260, 10265249568536, 39491671919840

Offset

2,2

Links

Michael De Vlieger, Table of n, a(n) for n = 2..1667

Paul Drube, Raised k-Dyck paths, arXiv:2206.01194 [math.CO], 2022. See Appendix pp. 14-15.

Formula

From Ralf Stephan, Jan 09 2005: (Start)

a(n) = C(2*n-1, n-2) - C(2*n-1, n-6).

G.f.: (1+x^2C^4)*C^5, where C=(1-sqrt(1-4*x))/(2*x). (End)

Conjecture: (13*n+118)*(n+5)*a(n) +(13*n^2-969*n-3490)*a(n-1) +2*(-203*n^2+1080*n+758)*a(n-2) +4*(73*n-182)*(2*n-5)*a(n-3)=0. - R. J. Mathar, Jun 22 2013

Mathematica

Table[Binomial[2*n - 1, n - 2] - Binomial[2*n - 1, n - 6], {n, 2, 25}] (* Michael De Vlieger, Jan 21 2026 *)

Crossrefs

Cf. A026022.

Sequence in context: A146585 A351363 A215008 * A002054 A289797 A246986

Adjacent sequences: A026024 A026025 A026026 * A026028 A026029 A026030

Keyword

nonn

Author

Clark Kimberling

Status

approved