A378937 Number of minimal edge cuts in the 2 X n rook graph.

1, 6, 22, 84, 346, 1476, 6322, 26844, 112666, 467796, 1925122, 7867404, 31980586, 129475716, 522603922, 2104600764, 8461122106, 33972973236, 136278002722, 546271650924, 2188568145226, 8764722448356, 35090249881522, 140455100761884, 562102748697946, 2249258115629076

Offset: 1

Author

Andrew Howroyd, Dec 12 2024

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 A378935.

Cf. A134165.

Programs

Mathematica

LinearRecurrence[{10, -35, 50, -24}, {1, 6, 22, 84}, 30] (* Paolo Xausa, Mar 02 2025 *)

PARI

a(n) = 2^(2*n-1) - 3^n + 5*2^(n-1) - 3

Formula

a(n) = A134165(n) - 2.

a(n) = 2^(2*n-1) - 3^n + 5*2^(n-1) - 3.

G.f.: (1 - 4*x - 3*x^2 + 24*x^3)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)).

E.g.f.: exp(x)*(2*exp(3*x) - 3*exp(2*x) + 5*exp(x) - 3). - Stefano Spezia, Mar 03 2025