A360201 Number of induced paths in the n-ladder graph P_2 X P_n.

1, 8, 25, 58, 117, 218, 387, 666, 1123, 1868, 3079, 5044, 8229, 13388, 21741, 35262, 57145, 92558, 149863, 242590, 392631, 635408, 1028235, 1663848, 2692297, 4356368, 7048897, 11405506, 18454653, 29860418, 48315339, 78176034, 126491659, 204667988

Offset: 1

Author

Andrew Howroyd, Jan 29 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 (3,-2,-1,1)

Crossrefs

Row 2 of A360199.

Programs

Mathematica

LinearRecurrence[{3,-2,-1,1},{1,8,25,58},40] (* Harvey P. Dale, Dec 28 2023 *)

PARI

Vec((1 + 5*x + 3*x^2)/((1 - x)^2*(1 - x - x^2)) + O(x^40))

Formula

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n > 4.

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