A391826 Number of partitions of the vertices of the n-ladder graph into dominating sets.

2, 4, 13, 35, 113, 368, 1182, 3838, 12463, 40429, 131269, 426262, 1384198, 4495620, 14602111, 47431703, 154081177, 500554852, 1626190314, 5283311170, 17165381859, 55771348385, 181208069377, 588777467930, 1913070123762, 6216066591424, 20197827114603, 65629208681235

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Ladder Graph.

Index entries for linear recurrences with constant coefficients, signature (6,-9,3,-18,31,-6,2,-16,8).

Formula

G.f.: x*(2 - 8*x + 7*x^2 - 13*x^3 + 44*x^4 - 24*x^5 + 8*x^6 - 34*x^7 + 20*x^8)/((1 - x)*(1 - 3*x - x^2 + 2*x^4)*(1 - 2*x - x^2 - 4*x^3 + 4*x^4)).

a(n) = 1 + A180762(n) + A230813(n)/2.

Prog

(PARI) Vec((2 - 8*x + 7*x^2 - 13*x^3 + 44*x^4 - 24*x^5 + 8*x^6 - 34*x^7 + 20*x^8)/((1 - x)*(1 - 3*x - x^2 + 2*x^4)*(1 - 2*x - x^2 - 4*x^3 + 4*x^4)) + O(x^30))

Crossrefs

Row 2 of A391824.

Cf. A180762, A230813, A391827.

Sequence in context: A192443 A189590 A189597 * A148235 A151522 A148236

Adjacent sequences: A391823 A391824 A391825 * A391827 A391828 A391829

Keyword

nonn

Author

Andrew Howroyd, Jan 10 2026

Status

approved