A359987 Number of edge cuts in the n-ladder graph P_2 X P_n.

1, 11, 105, 919, 7713, 63351, 514321, 4148839, 33347041, 267489431, 2143168305, 17160184519, 137349160833, 1099102033911, 8794224638161, 70360221445159, 562911076526881, 4503422288363351, 36027988077717105, 288226686123491719, 2305826176955087553, 18446667292472959671

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Edge Cut.

Eric Weisstein's World of Mathematics, Ladder Graph.

Index entries for linear recurrences with constant coefficients, signature (13,-42,16).

Formula

a(n) = 13*a(n-1) - 42*a(n-2) + 16*a(n-3) for n > 3.

a(n) = A013730(n-1) - A107839(n-1).

G.f.: x*(1 - 2*x + 4*x^2)/((1 - 8*x)*(1 - 5*x + 2*x^2)).

Mathematica

LinearRecurrence[{13, -42, 16}, {1, 11, 105}, 25] (* Paolo Xausa, Jun 24 2024 *)
Table[2^(3 n - 2) + (((5 - Sqrt[17])/2)^n - ((5 + Sqrt[17])/2)^n)/Sqrt[17], {n, 20}] // Expand (* Eric W. Weisstein, Nov 03 2024 *)
CoefficientList[Series[-(1 - 2 x + 4 x^2)/((-1 + 8 x) (1 - 5 x + 2 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 03 2024 *)

Prog

(PARI) Vec((1 - 2*x + 4*x^2)/((1 - 8*x)*(1 - 5*x + 2*x^2)) + O(x^25))

Crossrefs

Row 2 of A359990.

Cf. A013730, A107839, A356828 (vertex cuts), A359989.

Cf. A359621, A359622.

Sequence in context: A158470 A372146 A163933 * A377641 A099839 A287834

Adjacent sequences: A359984 A359985 A359986 * A359988 A359989 A359990

Keyword

nonn,easy

Author

Andrew Howroyd, Jan 28 2023

Status

approved