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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
Eric Weisstein's World of Mathematics, Total Dominating Set
Eric Weisstein's World of Mathematics, Triangular Snake Graph
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
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 March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)