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A284699
Number of dominating sets in the n-antiprism graph.
7
3, 15, 57, 223, 863, 3333, 12883, 49791, 192441, 743775, 2874655, 11110405, 42941187, 165965647, 641449337, 2479171199, 9581878847, 37033506309, 143132741651, 553201243263, 2138096511097, 8263641389887, 31938581194175, 123441098248197, 477093977471363, 1843945546253839, 7126761892007865
OFFSET
1,1
COMMENTS
Recurrence used to extrapolate sequence to a(1) and a(2).
LINKS
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Dominating Set
FORMULA
From Colin Barker, Apr 01 2017: (Start)
G.f.: x*(3 + 6*x + 3*x^2 + 4*x^3 + 5*x^4) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5).
a(n) = 3*a(n-1) + 3*a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>5.
(End)
MATHEMATICA
LinearRecurrence[{3, 3, 1, 1, 1}, {3, 15, 57, 223, 863, 3333, 12883}, 20]
Table[RootSum[-1 - # - #^2 - 3 #^3 - 3 #^4 + #^5 &, #^n &], {n, 20}]
PROG
(PARI) Vec(x*(3 + 6*x + 3*x^2 + 4*x^3 + 5*x^4) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5) + O(x^30)) \\ Colin Barker, Apr 01 2017
CROSSREFS
Sequence in context: A358685 A118048 A210448 * A218657 A218804 A125673
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 01 2017
STATUS
approved