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 A308591 Number of minimal total dominating sets in the (2n-1)-triangular snake graph. 1
 0, 3, 5, 7, 14, 22, 42, 70, 127, 218, 388, 675, 1191, 2083, 3663, 6420, 11275, 19777, 34716, 60912, 106904, 187592, 329213, 577716, 1013834, 1779141, 3122189, 5479045, 9615069, 16873254, 29610513, 51962811, 91188394, 160024458, 280823366, 492810634, 864822395 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Total Dominating Set Eric Weisstein's World of Mathematics, Triangular Snake Graph Index entries for linear recurrences with constant coefficients, signature (0,2,1,1,1). FORMULA From Andrew Howroyd, Sep 08 2019: (Start) a(n) = 2*a(n-2) + a(n-3) + a(n-4) + a(n-5) for n > 7. G.f.: x^2*(3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)). (End) MATHEMATICA Join[{0, 3}, Table[((3 - 5 n) (-1)^n + RootSum[-1 + # - 2 #^2 + #^3 &, -2 #^n + 249 #^(n + 1) + 7 #^(n + 2) &]/23)/25, {n, 3, 20}]] (* Eric W. Weisstein, Sep 19 2021 *) Join[{0, 3}, LinearRecurrence[{0, 2, 1, 1, 1}, {5, 7, 14, 22, 42}, 20]] (* Eric W. Weisstein, Sep 19 2021 *) CoefficientList[Series[x (-3 - 5 x - x^2 - x^3 + x^5)/((1 + x)^2 (-1 + 2 x - x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 19 2021 *) PROG (PARI) concat([0], Vec((3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)) + O(x^40))) \\ Andrew Howroyd, Sep 08 2019 CROSSREFS Sequence in context: A114980 A024372 A295717 * A309832 A319784 A346503 Adjacent sequences:  A308588 A308589 A308590 * A308592 A308593 A308594 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jun 09 2019 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, Sep 08 2019 STATUS approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)