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A287430
Number of connected dominating sets in the 2n-crossed prism graph.
2
115, 1063, 9121, 75607, 611569, 4857223, 38034241, 294475447, 2258978449, 17196401383, 130059675361, 978211787287, 7322040929329, 54576195433543, 405286730532481, 2999780651211127, 22137879320864209, 162941058582753703, 1196418733436205601
OFFSET
2,1
LINKS
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Crossed Prism Graph
FORMULA
From Andrew Howroyd, Sep 05 2017: (Start)
a(n) = 7^n + 240*n*7^(n-3) for n > 2.
a(n) = 14*a(n-1) - 49*a(n-2) for n > 4.
G.f.: x^2*(115 - 547*x - 126*x^2)/(1 - 7*x)^2.
(End)
MATHEMATICA
Join[{115}, Table[7^(n - 3) (343 + 240 n), {n, 3, 20}]]
LinearRecurrence[{14, -49}, {115, 1063, 9121}, 19] (* amended by Georg Fischer, Apr 03 2019 *)
CoefficientList[Series[(115 - 547 x - 126 x^2)/(-1 + 7 x)^2, {x, 0, 20}], x]
PROG
(PARI) Vec((115 - 547*x - 126*x^2)/(1 - 7*x)^2 + O(x^20)) \\ Andrew Howroyd, Sep 05 2017
CROSSREFS
Sequence in context: A251215 A218324 A258673 * A256889 A256354 A005466
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, May 25 2017
EXTENSIONS
Terms a(6) and beyond from Andrew Howroyd, Sep 05 2017
STATUS
approved