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URL: https://oeis.org/A302506

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A302506
Number of total dominating sets in the n-pan graph.
2
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
Eric Weisstein's World of Mathematics, Pan Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 09 2018
STATUS
approved