A374555 Number of maximal independent vertex sets in the n-flower graph.

1, 9, 28, 61, 181, 552, 1569, 4445, 12844, 36699, 104765, 300004, 858001, 2453607, 7018828, 20076509, 57423893, 164253216, 469821969, 1343844751, 3843853692, 10994731647, 31448643453, 89953775588, 257298299681, 735960275319, 2105095708540, 6021286996219, 17222920703093, 49263388094682

Offset

1,2

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, Maximal Independent Vertex Set.

Index entries for linear recurrences with constant coefficients, signature (1,4,5,-2,-7,2,15,6,-5,1,6,3,-3,-1).

Formula

G.f.: x*(1 + 8*x + 15*x^2 - 8*x^3 - 35*x^4 + 12*x^5 + 105*x^6 + 48*x^7 - 45*x^8 + 10*x^9 + 66*x^10 + 36*x^11 - 39*x^12 - 14*x^13)/((1 + x)*(1 - x + x^4)*(1 + x + x^4)*(1 - 2*x - x^2 - 5*x^3 + 2*x^4 + x^5)). - Andrew Howroyd, May 24 2025

a(n) = a(n-1) + 4*a(n-2) + 5*a(n-3) - 2*a(n-4) - 7*a(n-5) + 2*a(n-6) + 15*a(n-7) + 6*a(n-8) - 5*a(n-9) + a(n-10) + 6*a(n-11) + 3*a(n-12) - 3*a(n-13) - a(n-14). - Wesley Ivan Hurt, May 15 2026

Crossrefs

Cf. A366516.

Sequence in context: A366863 A135705 A321559 * A041359 A034126 A034677

Adjacent sequences: A374552 A374553 A374554 * A374556 A374557 A374558

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2024

Extensions

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

Status

approved