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

Author

Eric W. Weisstein, Apr 12 2018

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A213661, A290270, A302603.

Programs

Mathematica

Join[{1, 5}, Table[(-720 + 2732 n - 1880 n^2 + 505 n^3 - 40 n^4 + 3 n^5)/120, {n, 3, 20}]]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 5, 14, 44, 112, 238, 449, 782}, 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]

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.

Extensions

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