A378935 -id:A378935 - cp's OEIS frontend

A378936 Number of minimal edge cuts in the n X n rook graph.

0, 6, 150, 23214, 14673870, 32893769886, 277707579785790, 9185104346133530814, 1207381826962079773424430, 633579118339962549031587426846, 1329073084589877793324888678089108990, 11149987705045482483752338599907193464092414, 374140639230104433076704980495741968217315823513390

Offset: 1

Andrew Howroyd, Dec 12 2024

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..50
Eric Weisstein's World of Mathematics, Minimal Edge Cut.
Eric Weisstein's World of Mathematics, Rook Graph.

Main diagonal of A378935.

Cf. A286189.

a(n) = A286189(n) + (2^(n-1)-1)^2 - 2^(n^2-1).

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

Original entry on oeis.org

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

Andrew Howroyd, Dec 12 2024

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

Row 2 of A378935.

Cf. A134165.

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
```

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

cp's OEIS Frontend

A378936 Number of minimal edge cuts in the n X n rook graph.

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