A378848 Number of edge covers in the n-Plummer-Toft graph.

26, 263, 2187, 17304, 133369, 1015455, 7687086, 58033771, 437563871, 3297146264, 24837633069, 187078211139, 1408991309974, 10611584316423, 79918238982579, 601878225366808, 4532835546280529, 34137415194318455, 257093438977730622, 1936204411856546547, 14581807054477379095

Offset

0,1

Comments

The sequence has been extended to n = 0 using the linear recurrence. This is consistent with the number of edge covers on the house graph which is the graph obtained from the first Plummer-Toft graph after removing 1 vertex with its 3 incident edges. - Andrew Howroyd, Dec 09 2024

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Edge Cover.

Eric Weisstein's World of Mathematics, Plummer-Toft Graph.

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

Formula

G.f.: (26 - 23*x - 82*x^2 + 105*x^3 + 178*x^4 + 56*x^5)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)). - Andrew Howroyd, Dec 09 2024

Prog

(PARI) Vec( (26 - 23*x - 82*x^2 + 105*x^3 + 178*x^4 + 56*x^5)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)) + O(x^25) ) \\ Andrew Howroyd, Dec 09 2024

Crossrefs

Cf. A377769, A378701.

Sequence in context: A136922 A136921 A042308 * A251673 A059744 A016106

Adjacent sequences: A378845 A378846 A378847 * A378849 A378850 A378851

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 09 2024

Extensions

a(0)=26 prepended and terms a(9) onwards by Andrew Howroyd, Dec 09 2024

Status

approved