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

1,3

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, Pan Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

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

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)

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]

Prog

(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

Crossrefs

Cf. A290273, A302506, A303005.

Sequence in context: A170949 A276953 A276943 * A228784 A082328 A082327

Adjacent sequences: A303145 A303146 A303147 * A303149 A303150 A303151

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 19 2018

Extensions

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

Status

approved