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

Author

Eric W. Weisstein, Jul 25 2017

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Programs

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]

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).