A302762 Number of minimal total dominating sets in the n-Andrásfai graph.

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

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

Eric Weisstein's World of Mathematics, Andrásfai 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