A290273 Number of minimal dominating sets in the n-pan graph.

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

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

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

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 A357381 A061565

Adjacent sequences: A290270 A290271 A290272 * A290274 A290275 A290276

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 25 2017

Status

approved