A360848 Number of dominating induced trees in the n-ladder graph P_2_X P_n.

3, 8, 17, 32, 66, 130, 262, 522, 1046, 2090, 4182, 8362, 16726, 33450, 66902, 133802, 267606, 535210, 1070422, 2140842, 4281686, 8563370, 17126742, 34253482, 68506966, 137013930, 274027862, 548055722, 1096111446, 2192222890, 4384445782, 8768891562

Offset: 1

Author

Andrew Howroyd, Feb 23 2023

Keywords

• nonn
• easy

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 (1,2).

Crossrefs

Row 2 of A360846.

Programs

Mathematica

LinearRecurrence[{1, 2}, {3, 8, 17, 32}, 50] (* Paolo Xausa, Oct 03 2024 *)

PARI

Vec((3 + 5*x + 3*x^2 - x^3)/((1 + x)*(1 - 2*x)) + O(x^20))

Formula

a(n) = a(n-1) + 2*a(n-2) for n > 4.

G.f.: x*(3 + 5*x + 3*x^2 - x^3)/((1 + x)*(1 - 2*x)).