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A287063
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Number of dominating sets in the n-crown graph (for n > 1).
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2
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3, 9, 39, 183, 833, 3629, 15291, 63051, 256605, 1036401, 4167815, 16720031, 66986169, 268173525, 1073185011, 4293787923, 17177379125, 68714234201, 274866897279, 1099488559527, 4397998277073, 17592085381629, 70368534463019, 281474540503643, 1125899000873613
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OFFSET
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1,1
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COMMENTS
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The 1-crown graph is the 2-empty graph bar K_2 which has a single dominating set and so differs from a(1) = 3. - Eric W. Weisstein, Sep 04 2021
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LINKS
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FORMULA
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a(n) = 4^n - 2^n*(n + 2) + n^2 + n + 3.
G.f.: x*(3 - 24*x + 81*x^2 - 126*x^3 + 92*x^4 - 32*x^5) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)).
a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) - 16*a(n-6) for n>6.
(End)
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MATHEMATICA
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Table[4^n - 2^n (n + 2) + n^2 + n + 3, {n, 25}]
LinearRecurrence[{11, -47, 101, -116, 68, -16}, {3, 9, 39, 183, 833, 3629}, 25]
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PROG
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(PARI) Vec( x*(3 - 24*x + 81*x^2 - 126*x^3 + 92*x^4 - 32*x^5) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, May 19 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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