A366516 Number of independent vertex sets in the n-flower graph.

4, 44, 178, 1112, 6114, 35426, 201870, 1157984, 6627562, 37965284, 217412254, 1245183926, 7131222570, 40841504468, 233903535198, 1339592973824, 7671999302986, 43938415670258, 251640290080798, 1441172550842432, 8253758901579306, 47270215093528196, 270721892406133662, 1550455037141580710

Offset

1,1

Comments

The n-flower graph can be defined without using parallel edges for n >= 3. It is a snark for odd n >= 5. The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 24 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Flower Graph.

Eric Weisstein's World of Mathematics, Independent Vertex Set.

Index entries for linear recurrences with constant coefficients, signature (4,14,-18,-36,22,17,-6,-2).

Formula

G.f.: 2*x*(2 + 14*x - 27*x^2 - 72*x^3 + 55*x^4 + 51*x^5 - 21*x^6 - 8*x^7)/((1 + x - x^2)*( 1 - x - x^2)*(1 - 4*x - 11*x^2 + 6*x^3 + 2*x^4)). - Andrew Howroyd, May 24 2025

Prog

(PARI) Vec(2*x*(2 + 14*x - 27*x^2 - 72*x^3 + 55*x^4 + 51*x^5 - 21*x^6 - 8*x^7)/((1 + x - x^2)*( 1 - x - x^2)*(1 - 4*x - 11*x^2 + 6*x^3 + 2*x^4)) + O(x^25)) \\ Andrew Howroyd, May 24 2025

Crossrefs

Cf. A374555.

Sequence in context: A053314 A051223 A330651 * A353542 A265081 A077435

Adjacent sequences: A366513 A366514 A366515 * A366517 A366518 A366519

Keyword

nonn,easy

Author

Eric W. Weisstein, Oct 11 2023

Extensions

a(1)-a(4) and a(21) onwards from Andrew Howroyd, May 24 2025

Status

approved