A359988 Number of edge cuts in the 3 X n grid graph.

3, 105, 3665, 123215, 4051679, 131630449, 4248037953, 136587740399, 4382607093471, 140457446235441, 4498520188148993, 144023056568886959, 4610014925578108703, 147543642097619999089, 4721816707356538941633, 151105755554498621737583, 4835522406931884652356447

Offset: 1

Author

Andrew Howroyd, Jan 28 2023

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (54,-777,2390,-1736,256).

Crossrefs

Row 3 of A359990.

Cf. A013823, A158453, A359987.

Programs

PARI

Vec((3 - 57*x + 326*x^2 - 280*x^3 + 32*x^4)/((1 - 32*x)*(1 - 22*x + 73*x^2 - 54*x^3 + 8*x^4)) + O(x^20))

Formula

a(n) = 54*a(n-1) - 777*a(n-2) + 2390*a(n-3) - 1736*a(n-4) + 256*a(n-5) for n > 5.

G.f.: x*(3 - 57*x + 326*x^2 - 280*x^3 + 32*x^4)/((1 - 32*x)*(1 - 22*x + 73*x^2 - 54*x^3 + 8*x^4)).

a(n) = A013823(n-1) - A158453(n).