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A303072 Number of minimal total dominating sets in the n-ladder graph. 2
1, 4, 4, 16, 16, 49, 81, 169, 324, 625, 1296, 2401, 4900, 9409, 18769, 36481, 71824, 141376, 276676, 544644, 1067089, 2099601, 4116841, 8088336, 15880225, 31181056, 61230625, 120209296, 236083225, 463497841, 910168561, 1787091076, 3509140644, 6890328064, 13529411856 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Ladder Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (-1,1,3,7,8,2,6,6,0,0,-6,-6,-2,-8,-7,-3,-1,1,1).

FORMULA

a(n) = A253412(n)^2.

G.f.: x*(-1 - 5*x - 7*x^2 - 13*x^3 - 9*x^4 - x^5 - 4*x^6 + 5*x^7 + 13*x^8 + 14*x^9 + 21*x^10 + 15*x^11 + 12*x^12 + 15*x^13 + 9*x^14 + 3*x^15 - 2*x^17 - x^18)/(-1 - x + x^2 + 3*x^3 + 7*x^4 + 8*x^5 + 2*x^6 + 6*x^7 + 6*x^8 - 6*x^11 - 6*x^12 - 2*x^13 - 8*x^14 - 7*x^15 - 3*x^16 - x^17 + x^18 + x^19).

MATHEMATICA

Table[(RootSum[1 - #^2 - #^3 - #^4 + #^6 &, (9 - 18 #^2 + 23 #^3 - 3 #^4 + 32 #^5) #^n &]/229)^2, {n, 40}]

LinearRecurrence[{-1, 1, 3, 7, 8, 2, 6, 6, 0, 0, -6, -6, -2, -8, -7, -3, -1, 1, 1}, {1, 4, 4, 16, 16, 49, 81, 169, 324, 625, 1296, 2401, 4900, 9409, 18769, 36481, 71824, 141376, 276676}, 40]

CoefficientList[Series[(-1 - 5 x - 7 x^2 - 13 x^3 - 9 x^4 - x^5 - 4 x^6 + 5 x^7 + 13 x^8 + 14 x^9 + 21 x^10 + 15 x^11 + 12 x^12 + 15 x^13 + 9 x^14 + 3 x^15 - 2 x^17 - x^18)/(-1 - x + x^2 + 3 x^3 + 7 x^4 + 8 x^5 + 2 x^6 + 6 x^7 + 6 x^8 - 6 x^11 - 6 x^12 - 2 x^13 - 8 x^14 - 7 x^15 - 3 x^16 - x^17 + x^18 + x^19), {x, 0, 40}], x]

CROSSREFS

Row 2 of A303118.

Cf. A290379, A302402, A303054.

Sequence in context: A220761 A278238 A218522 * A231839 A141125 A164111

Adjacent sequences:  A303069 A303070 A303071 * A303073 A303074 A303075

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 18 2018

STATUS

approved

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Last modified October 24 16:24 EDT 2021. Contains 348233 sequences. (Running on oeis4.)