A303148 Number of minimal total dominating sets in the n-pan graph.

1, 1, 3, 2, 4, 8, 6, 6, 13, 18, 20, 28, 37, 45, 65, 91, 111, 144, 200, 264, 346, 464, 609, 798, 1072, 1428, 1873, 2479, 3297, 4361, 5779, 7670, 10140, 13416, 17806, 23598, 31229, 41374, 54820, 72600, 96197, 127465, 168801, 223587, 296255, 392460, 519856

Offset: 1

Author

Eric W. Weisstein, Apr 19 2018

Keywords

• nonn
• easy

Comments

Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Apr 19 2018

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Minimal Total Dominating Set.
• Eric Weisstein's World of Mathematics, Pan Graph.
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,1,0,-1,-1).

Crossrefs

Cf. A290273, A302506, A347650.

Programs

Mathematica

LinearRecurrence[{0, 0, 1, 1, 1, 1, 0, -1, -1}, {1, 1, 3, 2, 4, 8, 6, 6, 13}, 20]
CoefficientList[Series[(1 + x + 3 x^2 + x^3 + 2 x^4 + 3 x^5 - x^6 - 4 x^7 - 3 x^8)/(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9), {x, 0, 20}], x]

PARI

Vec((1 + x + 3*x^2 + x^3 + 2*x^4 + 3*x^5 - x^6 - 4*x^7 - 3*x^8)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^40)) \\ Andrew Howroyd, Apr 19 2018

Formula

From Andrew Howroyd, Apr 19 2018: (Start)

a(n) = a(n-3) + a(n-4) + a(n-5) + a(n-6) - a(n-8) - a(n-9) for n > 9.

G.f.: x*(1 + x + 3*x^2 + x^3 + 2*x^4 + 3*x^5 - x^6 - 4*x^7 - 3*x^8)/((1 - x^2 - x^3)*(1 + x^2 - x^6)). (End)

Extensions

a(1)-a(2) and terms a(20) and beyond from Andrew Howroyd, Apr 19 2018