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A303148 Number of minimal total dominating sets in the n-pan graph. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)