A302506 Number of total dominating sets in the n-pan graph.

2, 3, 7, 12, 17, 27, 46, 75, 119, 192, 313, 507, 818, 1323, 2143, 3468, 5609, 9075, 14686, 23763, 38447, 62208, 100657, 162867, 263522, 426387, 689911, 1116300, 1806209, 2922507, 4728718, 7651227, 12379943, 20031168, 32411113, 52442283, 84853394, 137295675

Offset

1,1

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Pan Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).

Formula

5*a(n) = 3*A000032(n+2) + 6*cos(n*Pi/2) - 2*sin(n*Pi/2).

a(n) = a(n-1) + a(n-2) + a(n-3) for n > 3.

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

E.g.f.: (6*cos(x) - 2*sin(x) - 15 + 3*exp(x/2)*(3*cosh(sqrt(5)*x/2) + sqrt(5)*sinh(sqrt(5)*x/2)))/5. - Stefano Spezia, Jan 03 2023

Mathematica

Table[(3 LucasL[n + 2] + 6 Cos[n Pi/2] - 2 Sin[n Pi/2])/5, {n, 20}]
LinearRecurrence[{1, 0, 1, 1}, {2, 3, 7, 12}, 20]
CoefficientList[Series[(-2 - x - 4 x^2 - 3 x^3)/(-1 + x + x^3 + x^4), {x, 0, 20}], x]

Crossrefs

Cf. A000032.

Sequence in context: A128458 A066733 A049623 * A228828 A061577 A350437

Adjacent sequences: A302503 A302504 A302505 * A302507 A302508 A302509

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 09 2018

Status

approved