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A302655 Number of minimal total dominating sets in the n-path graph. 4
0, 1, 2, 1, 2, 4, 3, 4, 8, 9, 10, 16, 21, 25, 36, 49, 60, 81, 112, 144, 189, 256, 336, 441, 592, 784, 1029, 1369, 1820, 2401, 3182, 4225, 5586, 7396, 9815, 12996, 17200, 22801, 30210, 40000, 53001, 70225, 93000, 123201, 163240, 216225, 286416, 379456, 502665 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Path Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,1,0,-1,-1).

FORMULA

From Andrew Howroyd, Apr 15 2018: (Start)

a(n) = a(n-3) + a(n-4) + a(n-5) + a(n-6) - a(n-8) - a(n-9) for n > 9.

G.f.: x^2*(1 + 2*x + x^2 + x^3 + x^4 - x^5 - 2*x^6 - x^7)/(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9).

a(2*n) = A000931(n+5)^2. (End)

MATHEMATICA

Table[If[Mod[n, 2] == 0, (RootSum[-1 - # + #^3 &, #^(n/2 + 5) (5 - 6 # + 4 #^2) &]/23)^2, (RootSum[-1 + # - 2 #^2 + #^3 &, #^((n - 1)/2) (4 - 2 # + 5 #^2) &] + RootSum[-1 + #^2 + #^3 &, #^((n - 1)/2) (-5 + 6 # + 3 #^2) &])/23], {n, 50}]

LinearRecurrence[{0, 0, 1, 1, 1, 1, 0, -1, -1}, {0, 1, 2, 1, 2, 4, 3,

  4, 8}, 50]

CoefficientList[Series[(x (1 + 2 x + x^2 + x^3 + x^4 - x^5 - 2 x^6 - x^7))/(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9), {x, 0, 50}], x]

PROG

(PARI) concat([0], Vec(x^2*(1 + 2*x + x^2 + x^3 + x^4 - x^5 - 2*x^6 - x^7)/(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9) + O(x^50))) \\ Andrew Howroyd, Apr 15 2018

CROSSREFS

Row 1 of A303118.

Cf. A000931, A300738, A302654.

Sequence in context: A238577 A131380 A100461 * A316997 A323465 A124904

Adjacent sequences:  A302652 A302653 A302654 * A302656 A302657 A302658

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Apr 11 2018

EXTENSIONS

Terms a(20) and beyond from Andrew Howroyd, Apr 15 2018

STATUS

approved

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)