A360874 Number of (non-null) connected induced subgraphs in the 2 X n rook graph.

3, 13, 51, 205, 843, 3493, 14451, 59485, 243483, 991573, 4021251, 16253965, 65530923, 263685253, 1059458451, 4252051645, 17050991163, 68332580533, 273716694051, 1096026940525, 4387590352203, 17560813373413, 70274617776051, 281192580728605, 1125052685342043

Offset: 1

Author

Andrew Howroyd, Feb 24 2023

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Crossrefs

Row 2 of A360873.

Cf. A360876.

Programs

Mathematica

LinearRecurrence[{10, -35, 50, -24}, {3, 13, 51, 205}, 30] (* Paolo Xausa, Oct 03 2024 *)

PARI

Vec((3 - 17*x + 26*x^2)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) + O(x^25))

Formula

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n > 4.

G.f.: x*(3 - 17*x + 26*x^2)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)).