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..1000
Eric Weisstein's World of Mathematics, Flower Graph.
Eric Weisstein's World of Mathematics, Minimum Connected Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (0,7,0,-3,0,-55,0,7,0,315,0,70,0,-1000,0,-630,0,1780,0,1691,0,-1587,0,-1782,0,540,0,648).
FORMULA
G.f.: x*(1 + 9*x - x^2 + 156*x^3 - 19*x^4 + 462*x^5 - 11*x^6 - 1845*x^7 + 135*x^8 - 5079*x^9 + 255*x^10 + 777*x^11 - 220*x^12 + 20163*x^13 - 1040*x^14 + 7857*x^15 - 650*x^16 - 31626*x^17 + 1040*x^18 - 32937*x^19 + 1509*x^20 + 25035*x^21 + 81*x^22 + 32364*x^23 - 756*x^24 + 15336*x^25 - 324*x^26 + 7128*x^27)/(((1 - x)^2*(1 + x)^2*(1 + x^2)^3*(1 - 2*x^2)^3*(1 - x - 3*x^3)^2*(1 + x + 3*x^3)^2)). - Andrew Howroyd, May 24 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 29 2025
EXTENSIONS
a(1)-a(4) and a(10) onwards from Andrew Howroyd, May 24 2025
STATUS
approved