A303072 Number of minimal total dominating sets in the n-ladder graph.

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

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