A332392 Number of minimal total dominating sets in the 2 X n king graph.

1, 1, 6, 10, 15, 52, 105, 175, 481, 1028, 2000, 4821, 10368, 21285, 48625, 105889, 224578, 498106, 1084331, 2331760, 5121797, 11162455, 24152665, 52751528, 114914016, 249490481, 543949956, 1184591233, 2575134753, 5608825345, 12212701582, 26569155354, 57849402071

Offset: 0

Author

Andrew Howroyd, Feb 10 2020

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, King Graph.
• Eric Weisstein's World of Mathematics, Minimal Total Dominating Set.
• Index entries for linear recurrences with constant coefficients, signature (0,1,5,4,8,16,-8,-48,-64).

Crossrefs

Row n=2 of A332390.

Programs

PARI

Vec((1 + x + 5*x^2 + 4*x^3 - 8*x^6 - 48*x^7 - 64*x^8)/(1 - x^2 - 5*x^3 - 4*x^4 - 8*x^5 - 16*x^6 + 8*x^7 + 48*x^8 + 64*x^9) + O(x^40))

Formula

a(n) = a(n-2) + 5*a(n-3) + 4*a(n-4) + 8*a(n-5) + 16*a(n-6) - 8*a(n-7) - 48*a(n-8) - 64*a(n-9) for n >= 9.

G.f.: (1 + x + 5*x^2 + 4*x^3 - 8*x^6 - 48*x^7 - 64*x^8)/(1 - x^2 - 5*x^3 - 4*x^4 - 8*x^5 - 16*x^6 + 8*x^7 + 48*x^8 + 64*x^9).