A302759 Number of total dominating sets in the n-Andrásfai graph.

1, 11, 131, 1365, 12883, 113935, 967455, 8013983, 65410751, 529283583, 4261449727, 34213027327, 274240586751, 2196272295935, 17580376055807, 140687025184767, 1125685164621823, 9006288735567871, 72053745778425855, 576444534576513023, 4611617848860868607

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Eric Weisstein's World of Mathematics, Andrásfai Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (23,-210,996,-2664,4032,-3200,1024).

Formula

a(n) = (8^(n + 1) + (2^n*(n - 2) - 4^(n + 1))*(3*n - 1))/16 - 1 for n > 1.

a(n) = 23*a(n-1) - 210*a(n-2) + 996*a(n-3) - 2664*a(n-4) + 4032*a(n-5) - 3200*a(n-6) + 1024*a(n-7) for n > 8.

G.f.: x*(-1 + 12*x - 88*x^2 + 334*x^3 - 706*x^4 + 928*x^5 - 672*x^6 + 256*x^7)/((-1 + 2*x)^3*(-1 + 4*x)^2*(1 - 9*x + 8*x^2)).

Mathematica

Join[{1}, Table[(8^(n + 1) + (2^n (n - 2) - 4^(n + 1) ) (3 n - 1) - 16)/16, {n, 2, 20}]]
Join[{1}, LinearRecurrence[{23, -210, 996, -2664, 4032, -3200, 1024}, {11, 131, 1365, 12883, 113935, 967455, 8013983}, 20]]
CoefficientList[Series[(-1 + 12 x - 88 x^2 + 334 x^3 - 706 x^4 + 928 x^5 - 672 x^6 + 256 x^7)/((-1 + 2 x)^3 (-1 + 4 x)^2 (1 - 9 x + 8 x^2)), {x, 0, 20}], x]

Crossrefs

Cf. A285272, A287429, A302762.

Sequence in context: A185127 A287295 A227677 * A076255 A076357 A015606

Adjacent sequences: A302756 A302757 A302758 * A302760 A302761 A302762

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 12 2018

Extensions

a(9)-a(21) from Andrew Howroyd, Apr 18 2018

Status

approved