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

0,3

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).

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).

Mathematica

LinearRecurrence[{0, 1, 5, 4, 8, 16, -8, -48, -64}, {1, 1, 6, 10, 15, 52, 105, 175, 481}, 35] (* Paolo Xausa, Jul 07 2026 *)

Prog

(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))

Crossrefs

Row n=2 of A332390.

Sequence in context: A020159 A357529 A048017 * A048078 A229276 A319035

Adjacent sequences: A332389 A332390 A332391 * A332393 A332394 A332395

Keyword

nonn,easy

Author

Andrew Howroyd, Feb 10 2020

Status

approved