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A302506 Number of total dominating sets in the n-pan graph. 1
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 (list; graph; refs; listen; history; text; internal format)
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).

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

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

Sequence in context: A128458 A066733 A049623 * A228828 A061577 A006488

Adjacent sequences:  A302503 A302504 A302505 * A302507 A302508 A302509

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 09 2018

STATUS

approved

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Last modified May 16 12:30 EDT 2021. Contains 343947 sequences. (Running on oeis4.)