A359622 Number of edge cuts in the n-Moebius ladder.

1, 26, 307, 3004, 27049, 232658, 1947103, 16021784, 130447957, 1055068574, 8498016971, 68269451044, 547562782017, 4387403277994, 35132904838583, 281226897433648, 2250607478637613, 18008682685966262, 144087851840540835, 1152791046751807804, 9222750661998396185, 73784021962658308290

Offset: 1

Author

Eric W. Weisstein, Jan 07 2023

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Edge Cut
• Eric Weisstein's World of Mathematics, Moebius Ladder
• Index entries for linear recurrences with constant coefficients, signature (20,-146,488,-777,612,-228,32).

Programs

Mathematica

Table[With[{a = 5 - Sqrt[17], b = 5 + Sqrt[17]}, 1 + 8^n - n - ((n + 2) (a^n + b^n) - n (b^n - a^n)/Sqrt[17])/2^(n + 1)], {n, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
LinearRecurrence[{20, -146, 488, -777, 612, -228, 32}, {1, 26, 307, 3004, 27049, 232658, 1947103}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 + 6 x - 67 x^2 + 172 x^3 - 120 x^4 + 36 x^5)/((-1 + x)^2 (-1 + 8 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

PARI

Vec((1 + 6*x - 67*x^2 + 172*x^3 - 120*x^4 + 36*x^5)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2) + O(x^20)) \\ Andrew Howroyd, Jan 26 2023

Formula

G.f.: x*(1 + 6*x - 67*x^2 + 172*x^3 - 120*x^4 + 36*x^5)/((1 - x)^2*(1 - 8*x)*(1 - 5*x + 2*x^2)^2). - Andrew Howroyd, Jan 26 2023

Extensions

a(1)-a(2) prepended and terms a(8) and beyond from Andrew Howroyd, Jan 26 2023