A260769 Certain directed lattice paths.

1, 3, 15, 84, 491, 2948, 18018, 111520, 696739, 4384668, 27753110, 176494640, 1126809230, 7217773800, 46364184420, 298554038144, 1926593569059, 12455864623020, 80664529969422, 523165672201744, 3397648036150426, 22092460470618328, 143809661629562460

Offset

0,2

Comments

See Dziemianczuk (2014) for precise definition.

Links

Lars Blomberg, Table of n, a(n) for n = 0..100

M. Dziemianczuk, On Directed Lattice Paths With Additional Vertical Steps, arXiv preprint arXiv:1410.5747 [math.CO], 2014.

Formula

See Dziemianczuk (2014) Equation (29a) with m=0.

From Vaclav Kotesovec, Jul 15 2022: (Start)

Recurrence: (n-1)*n*(100*n^2 - 410*n + 411)*a(n) = -10*(n-1)*(8*n - 25)*a(n-1) + 4*(1100*n^4 - 6710*n^3 + 14571*n^2 - 13303*n + 4267)*a(n-2) - 120*(n-2)*(2*n - 1)*a(n-3) + 16*(n-3)*(n-2)*(100*n^2 - 210*n + 101)*a(n-4).

a(n) ~ sqrt(1 + sqrt(phi)) * 2^(n-1) * phi^(5*(2*n + 1)/4) / (5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. (End)

Crossrefs

Sequence in context: A115910 A355094 A106569 * A026032 A005809 A067122

Adjacent sequences: A260766 A260767 A260768 * A260770 A260771 A260772

Keyword

nonn

Author

N. J. A. Sloane, Jul 30 2015

Extensions

More terms from Lars Blomberg, Aug 01 2015

Status

approved