A296995 Number of edge covers in the n-dipyramidal graph.

2, 34, 341, 2902, 23092, 178393, 1359598, 10296846, 77752133, 586292914, 4418053928, 33282217873, 250685741074, 1888064403826, 14219675836741, 107091705316446, 806526755213324, 6074075885446057, 45744715781412614, 344509590254476102, 2594546978760459973

Offset

1,1

Comments

Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Jun 26 2018

Links

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

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Edge Cover

Index entries for linear recurrences with constant coefficients, signature (11, -24, -21, 33, 34, 8).

Formula

From Andrew Howroyd, Jun 26 2018: (Start)

a(n) = 11*a(n-1) - 24*a(n-2) - 21*a(n-3) + 33*a(n-4) + 34*a(n-5) + 8*a(n-6) for n > 6.

G.f.: x*(2 + 2*x + x^2)*(1 + 5*x + 2*x^2)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)). (End)

Mathematica

Table[LucasL[n] + 2^-n ((7 - Sqrt[65])^n + (7 + Sqrt[65])^n) - 2^(-n + 1) ((3 - Sqrt[17])^n + (3 + Sqrt[17])^n), {n, 20}] // Expand
LinearRecurrence[{11, -24, -21, 33, 34, 8}, {2, 34, 341, 2902, 23092, 178393}, 20]
CoefficientList[Series[(-2 - 12 x - 15 x^2 - 9 x^3 - 2 x^4)/(-1 + 11 x - 24 x^2 - 21 x^3 + 33 x^4 + 34 x^5 + 8 x^6), {x, 0, 20}], x]

Prog

(PARI) Vec((2 + 2*x + x^2)*(1 + 5*x + 2*x^2)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)) + O(x^30)) \\ Andrew Howroyd, Jun 26 2018

Crossrefs

Cf. A297713, A298822.

Sequence in context: A263689 A098531 A356342 * A301611 A224294 A092408

Adjacent sequences: A296992 A296993 A296994 * A296996 A296997 A296998

Keyword

nonn

Author

Eric W. Weisstein, Jun 18 2018

Extensions

a(1)-a(2) and terms a(11) and beyond from Andrew Howroyd, Jun 26 2018

Status

approved