A260770 Certain directed lattice paths.

1, 6, 35, 207, 1251, 7678, 47658, 298371, 1880659, 11918586, 75871710, 484793950, 3107494430, 19973075580, 128678167220, 830735862179, 5372968238979, 34807369089378, 225818672567382, 1466956891774602, 9540909022501226, 62119854068610436, 404854330511525580

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=1.

From Vaclav Kotesovec, Jul 15 2022: (Start)

Recurrence: (n-2)*n*(n+1)*(100*n^3 - 510*n^2 + 677*n - 111)*a(n) = -6*n*(40*n^3 - 5*n^2 - 586*n + 863)*a(n-1) + 4*(n-1)*(1100*n^5 - 6710*n^4 + 12387*n^3 - 3775*n^2 - 8723*n + 5448)*a(n-2) - 72*(n-2)*(n-1)*(10*n^2 - 5*n - 24)*a(n-3) + 16*(n-3)*(n-2)*(n-1)*(100*n^3 - 210*n^2 - 43*n + 156)*a(n-4).

a(n) ~ sqrt((4*phi^6 - 1)/5 + phi^(11/2)) * 2^(n-1) * phi^(5*n/2) / sqrt(Pi*n), where phi = A001622 is the golden ratio. (End)

Crossrefs

Sequence in context: A352972 A180033 A354134 * A262717 A144638 A291246

Adjacent sequences: A260767 A260768 A260769 * A260771 A260772 A260773

Keyword

nonn

Author

N. J. A. Sloane, Jul 30 2015

Extensions

More terms from Lars Blomberg, Aug 01 2015

Status

approved