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A290273 Number of minimal dominating sets in the n-pan graph. 1
2, 2, 3, 5, 7, 8, 13, 18, 25, 34, 49, 69, 95, 134, 188, 264, 368, 517, 725, 1015, 1422, 1993, 2794, 3913, 5484, 7685, 10769, 15089, 21144, 29630, 41518, 58178, 81523, 114237, 160075, 224308, 314317, 440442, 617177, 864830, 1211861, 1698141, 2379551, 3334390, 4672376 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Eric Weisstein's World of Mathematics, Pan Graph

FORMULA

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

G.f.: x*(2 + 2*x + x^2 + x^3 - 2*x^5)/(1 - x^2 - x^3 - x^4 + x^6).

MATHEMATICA

Table[-RootSum[1 - #^2 - #^3 - #^4 + #^6 &, -9 #^n + 33 #^(n + 1) - 23 #^(n + 2) - 45 #^(n + 3) - 38 #^(n + 4) + #^(n + 5) &]/229, {n, 20}]

LinearRecurrence[{0, 1, 1, 1, 0, -1}, {2, 2, 3, 5, 7, 8}, 50]

CoefficientList[Series[(2 + 2 x + x^2 + x^3 - 2 x^5)/(1 - x^2 - x^3 - x^4 + x^6), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A079953 A133393 A126881 * A125505 A061565 A077075

Adjacent sequences:  A290270 A290271 A290272 * A290274 A290275 A290276

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jul 25 2017

STATUS

approved

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Last modified December 7 19:20 EST 2021. Contains 349585 sequences. (Running on oeis4.)