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A302762
Number of minimal total dominating sets in the n-Andrásfai 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
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Andrásfai Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 12 2018
EXTENSIONS
a(8)-a(20) from Andrew Howroyd, Apr 15 2018
STATUS
approved