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

1,2

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).

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A014472 A066912 A000498 * A015800 A276285 A232064

Adjacent sequences: A359619 A359620 A359621 * A359623 A359624 A359625

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 07 2023

Extensions

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

Status

approved