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A291537
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a(n) = 8^n - 3*2^n + 5.
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3
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7, 57, 493, 4053, 32677, 261957, 2096773, 16776453, 134216197, 1073738757, 8589928453, 68719464453, 549755789317, 4398046461957, 35184371990533, 281474976514053, 2251799813292037, 18014398508695557, 144115188074283013, 1152921504603701253, 9223372036848484357
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OFFSET
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1,1
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COMMENTS
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Number of dominating sets in the n X n X n complete tripartite graph.
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LINKS
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FORMULA
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a(n) = 8^n - 3*2^n + 5.
a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3).
G.f.: x*(7 - 20*x + 48*x^2)/(1 - 11*x + 26*x^2 - 16*x^3).
E.g.f.: exp(8*x) - 3*exp(2*x) + 5*exp(x) - 3. - G. C. Greubel, Aug 26 2017
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MATHEMATICA
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Table[8^n - 3 2^n + 5, {n, 20}]
LinearRecurrence[{11, -26, 16}, {7, 57, 493}, 20]
CoefficientList[Series[(-7 + 20 x - 48 x^2)/(-1 + 11 x - 26 x^2 + 16 x^3), {x, 0, 20}], x]
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PROG
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(PARI) x='x+O('x^50); Vec(x*(7 - 20*x + 48*x^2)/(1 - 11*x + 26*x^2 - 16*x^3)) \\ G. C. Greubel, Aug 26 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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