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A290379
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Number of minimal dominating sets in the n-ladder graph.
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5
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2, 6, 7, 18, 39, 75, 155, 310, 638, 1295, 2624, 5339, 10853, 22069, 44836, 91134, 185259, 376542, 765331, 1555567, 3161843, 6426646, 13062506, 26550391, 53965428, 109688223, 222948193, 453156469, 921069708, 1872133138, 3805230243, 7734373962, 15720610559
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OFFSET
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1,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 1, 3, 4, 4, 1, 2, 3, 5, 4, 2).
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FORMULA
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a(n) = a(n-2) + 3*a(n-3) + 4*a(n-4) + 4*a(n-5) + a(n-6) + 2*a(n-7) + 3*a(n-8) + 5*a(n-9) + 4*a(n-10) + 2*a(n-11) for n > 11.
G.f.: x*(1+x)*(2 + 4*x + x^2 + 5*x^3 + x^4 + 3*x^5 + 5*x^6 + 3*x^7 + 2*x^8 + 2*x^9)/(1 - x^2 - 3*x^3 - 4*x^4 - 4*x^5 - x^6 - 2*x^7- 3*x^8 - 5*x^9 - 4*x^10 - 2*x^11).
(End)
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MATHEMATICA
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Table[-RootSum[-2 - 4 # - 5 #^2 - 3 #^3 - 2 #^4 - #^5 - 4 #^6 - 4 #^7 - 3 #^8 - #^9 + #^11 &, 621827501801 #^n - 301456826961 #^(n + 1) + 280366986955 #^(n + 2) - 1253389979482 #^(n + 3) + 843186094854 #^(n + 4) - 87555893434 #^(n + 5) + 236346312907 #^(n + 6) - 504072574383 #^(n + 7) + 231943645265 #^(n + 8) - 618185916584 #^(n + 9) + 290649224768 #^(n + 10) &]/2097121971853, {n, 20}] (* Eric W. Weisstein, Aug 04 2017 *)
LinearRecurrence[{0, 1, 3, 4, 4, 1, 2, 3, 5, 4, 2}, {2, 6, 7, 18, 39, 75, 155, 310, 638, 1295, 2624}, 20] (* Eric W. Weisstein, Aug 04 2017 *)
CoefficientList[Series[((1 + x) (2 + 4 x + x^2 + 5 x^3 + x^4 + 3 x^5 + 5 x^6 + 3 x^7 + 2 x^8 + 2 x^9))/(1 - x^2 - 3 x^3 - 4 x^4 - 4 x^5 - x^6 - 2 x^7 - 3 x^8 - 5 x^9 - 4 x^10 - 2 x^11), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 04 2017 *)
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PROG
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(PARI) Vec((1+x)*(2+4*x+x^2+5*x^3+x^4+3*x^5+5*x^6+3*x^7+2*x^8+2*x^9)/(1-x^2-3*x^3-4*x^4-4*x^5-x^6-2*x^7-3*x^8-5*x^9-4*x^10-2*x^11)+O(x^40)) \\ Andrew Howroyd, Aug 01 2017
(Magma) I:=[2, 6, 7, 18, 39, 75, 155, 310, 638, 1295, 2624]; [n le 11 select I[n] else Self(n-2)+3*Self(n-3)+4*Self(n-4)+4*Self(n-5)+Self(n-6)+2*Self(n-7)+3*Self(n-8)+5*Self(n-9)+4*Self(n-10)+2*Self(n-11): n in [1..40]]; // Vincenzo Librandi, Aug 04 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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