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A302946 Number of minimal (and minimum) total dominating sets in the 2n-crossed prism graph. 2
4, 36, 196, 1156, 6724, 39204, 228484, 1331716, 7761796, 45239076, 263672644, 1536796804, 8957108164, 52205852196, 304278004996, 1773462177796, 10336495061764, 60245508192804, 351136554095044, 2046573816377476, 11928306344169796, 69523264248641316 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Extended to a(1) using the formula/recurrence.

Since minimal and minimum total dominating sets are equivalent, the crossed prism graphs could be said to be "well totally dominated".

LINKS

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Eric Weisstein's World of Mathematics, Well-Covered Graph

Index entries for linear recurrences with constant coefficients, signature (5,5,-1).

FORMULA

From Andrew Howroyd, Apr 16 2018: (Start)

a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3).

G.f.: 4*x*(1 + 4*x - x^2)/((1 + x)*(1 - 6*x + x^2)).

a(n) = 4*A090390(n) = 4*A001333(n)^2. (End)

a(n) = 2*(chebyshevT(n,3) + (-1)^n). - Eric W. Weisstein, Apr 17 2018

a(n) = 4*(-1)^n*chebyshevT(n,i)^2, where i is the imaginary unit. - Eric W. Weisstein, Apr 17 2018

MATHEMATICA

Table[2 (ChebyshevT[n, 3] + (-1)^n), {n, 20}]

Table[4 (-1)^n ChebyshevT[n, I]^2, {n, 20}]

LinearRecurrence[{5, 5, -1}, {4, 36, 196}, 20]

CoefficientList[Series[-4 (-1 - 4 x + x^2)/(1 - 5 x - 5 x^2 + x^3), {x, 0, 20}], x]

PROG

(PARI) Vec(4*(1 + 4*x - x^2)/((1 + x)*(1 - 6*x + x^2)) + O(x^30)) \\ Andrew Howroyd, Apr 16 2018

(PARI) a(n) = 2*(polchebyshev(n, 1, 3) + (-1)^n); \\ Michel Marcus, Apr 17 2018

CROSSREFS

Cf. A001333, A090390, A287062, A291772, A302941.

Sequence in context: A270084 A272222 A263420 * A220436 A144888 A291643

Adjacent sequences:  A302943 A302944 A302945 * A302947 A302948 A302949

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 16 2018

EXTENSIONS

a(1) and terms a(6) and beyond from Andrew Howroyd, Apr 16 2018

STATUS

approved

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Last modified February 27 06:03 EST 2020. Contains 332299 sequences. (Running on oeis4.)