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

Author

N. J. A. Sloane, Jul 30 2015

Keywords

• nonn

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)

Extensions

More terms from Lars Blomberg, Aug 01 2015