A290470 Number of minimal edge covers in the n-Moebius ladder.

3, 7, 15, 59, 143, 367, 1039, 2755, 7395, 20007, 53727, 144635, 389535, 1048159, 2821535, 7595267, 20443523, 55029319, 148125295, 398712379, 1073232175, 2888862159, 7776059055, 20931132355, 56341155043, 151655701607, 408217663167, 1098815603707, 2957725352255

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Edge Cover

Eric Weisstein's World of Mathematics, Minimal Edge Cover

Eric Weisstein's World of Mathematics, Moebius Ladder

Index entries for linear recurrences with constant coefficients, signature (1, 2, 6, 2, 2, -2, -2, -1, 1).

Formula

From Andrew Howroyd, Aug 04 2017: (Start)

a(n) = a(n-1) + 2*a(n-2) + 6*a(n-3) + 2*a(n-4) + 2*a(n-5) - 2*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n > 9.

G.f.: x*(1 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)).

(End)

Mathematica

Table[2 Cos[n Pi/2] - RootSum[-1 + # + #^2 + #^3 &, #^n &] +
  RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, #^n &], {n, 20}]
LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {3, 7, 15, 59, 143, 367, 1039, 2755, 7395}, 20]
CoefficientList[Series[-(((1 + x) (-3 - x - x^2 + x^3) (-1 - 4 x^3 + 3 x^4))/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]

Prog

(PARI) Vec((1 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)) + O(x^30)) \\ Andrew Howroyd, Aug 04 2017

Crossrefs

Cf. A020866, A020877, A020878, A284710.

Sequence in context: A276969 A146448 A192169 * A268061 A298358 A023370

Adjacent sequences: A290467 A290468 A290469 * A290471 A290472 A290473

Keyword

nonn

Author

Eric W. Weisstein, Aug 03 2017

Extensions

a(1)-a(2) and terms a(9) and beyond from Andrew Howroyd, Aug 04 2017

Status

approved