A302603 Number of total dominating sets in the wheel graph on n nodes.

4, 2, 4, 11, 24, 42, 79, 156, 304, 587, 1144, 2246, 4419, 8712, 17224, 34131, 67744, 134642, 267919, 533636, 1063704, 2121627, 4233904, 8452686, 16880899, 33722192, 67380304, 134656931, 269146104, 538020762, 1075602319, 2150493996, 4299838144, 8597815787

Offset

1,1

Comments

Extended to a(1)-a(3) using the formula/recurrence.

Links

Table of n, a(n) for n=1..34.

Eric Weisstein's World of Mathematics, Total Dominating Set

Eric Weisstein's World of Mathematics, Wheel Graph

Index entries for linear recurrences with constant coefficients, signature (4, -5, 3, -2, -1, 2).

Formula

a(n) = A000032(n - 1) + 2*sin(n*Pi/2) + 2^(n - 1) - 1.

a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6).

G.f.: x*(-4+14*x-16*x^2+7*x^3+3*x^5-2*x^4) / ( (x-1)*(2*x-1)*(x^2+x-1)*(x^2+1) ).

Mathematica

Table[LucasL[n - 1] + 2 Sin[n Pi/2] + 2^(n - 1) - 1, {n, 20}]
LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 2, 4, 11, 24, 42}, 20]
CoefficientList[Series[(-4 + 14 x - 16 x^2 + 7 x^3 - 2 x^4 + 3 x^5)/(-1 + 4 x - 5 x^2 + 3 x^3 - 2 x^4 - x^5 + 2 x^6), {x, 0, 20}], x]

Crossrefs

Sequence in context: A051666 A011382 A011302 * A085689 A343317 A134434

Adjacent sequences: A302600 A302601 A302602 * A302604 A302605 A302606

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 10 2018

Status

approved