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A302762 Number of minimal total dominating sets in the n-Andrasfai graph. 1
1, 5, 14, 44, 112, 238, 449, 782, 1287, 2030, 3096, 4592, 6650, 9430, 13123, 17954, 24185, 32118, 42098, 54516, 69812, 88478, 111061, 138166, 170459, 208670, 253596, 306104, 367134, 437702, 518903, 611914, 717997, 838502, 974870, 1128636, 1301432, 1494990, 1711145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..39.

Eric Weisstein's World of Mathematics, Andrasfai Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = (-720 + 2732*n - 1880*n^2 + 505*n^3 - 40*n^4 + 3*n^5)/120 for n > 2.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 8.

G.f.: x*(1 - x - x^2 + 15*x^3 - 27*x^4 + 15*x^5 + 2*x^6 - x^7)/(-1 + x)^6.

MATHEMATICA

Join[{1, 5}, Table[(-720 + 2732 n - 1880 n^2 + 505 n^3 - 40 n^4 + 3 n^5)/120, {n, 3, 20}]

Join[{1, 5}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {14, 44, 112, 238, 449, 7827}, 20]]

CoefficientList[Series[(1 - x - x^2 + 15 x^3 - 27 x^4 + 15 x^5 + 2 x^6 - x^7)/(-1 + x)^6, {x, 0, 20}], x]

CROSSREFS

Cf. A213661, A290270, A302603.

Sequence in context: A327594 A034530 A125246 * A140796 A197212 A100059

Adjacent sequences:  A302759 A302760 A302761 * A302763 A302764 A302765

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 12 2018

EXTENSIONS

a(8)-a(20) from Andrew Howroyd, Apr 15 2018

STATUS

approved

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Last modified January 17 16:38 EST 2021. Contains 340246 sequences. (Running on oeis4.)