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A382500
Number of minimum connected dominating sets in the n-flower graph.
1
1, 9, 6, 219, 20, 1968, 56, 10779, 144, 52488, 352, 231984, 832, 977133, 1920, 3966699, 4352, 15720639, 9728, 61191312, 21504, 235009107, 47104, 893270016, 102400, 3367409412, 221184, 12609435873, 475136, 46953650535, 1015808, 174014499435, 2162688, 642287275092, 4587520, 2362247579547
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
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
Cf. A362807.
Sequence in context: A390835 A370151 A038296 * A383348 A058276 A184964
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