A302405 Total domination number of the n-prism graph.

0, 1, 2, 2, 4, 4, 4, 5, 6, 6, 8, 8, 8, 9, 10, 10, 12, 12, 12, 13, 14, 14, 16, 16, 16, 17, 18, 18, 20, 20, 20, 21, 22, 22, 24, 24, 24, 25, 26, 26, 28, 28, 28, 29, 30, 30, 32, 32, 32, 33, 34, 34, 36, 36, 36, 37, 38, 38, 40, 40, 40, 41, 42, 42, 44, 44, 44, 45, 46, 46, 48

Offset

0,3

Comments

Extended to a(0)-a(2) using the formula/recurrence.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Prism Graph

Eric Weisstein's World of Mathematics, Total Domination Number

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Formula

a(n) = a(n-1) + a(n-6) - a(n-7).

G.f.: x*(1 + x + 2*x^3)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5)).

a(n) = a(n-6) + 4. - Andrew Howroyd, Apr 17 2018

Mathematica

Table[(3 + (-1)^n + 4 n - Cos[n Pi/3] - 3 Cos[2 n Pi/3] - Sqrt[3] Sin[n Pi/3] + Sin[2 n Pi/3]/Sqrt[3])/6, {n, 0, 50}]
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 2, 2, 4, 4, 4, 5, 6}, {0, 50}]
CoefficientList[Series[x (1 + x + 2 x^3)/((-1 + x)^2 (1 + x + x^2 + x^3 + x^4 + x^5)), {x, 0, 50}], x]

Prog

(PARI) x='x+O('x^50); concat(0, Vec(x*(1+x+2*x^3)/((1-x)^2*(1+x+ x^2+x^3+ x^4+x^5)))) \\ G. C. Greubel, Apr 09 2018
(Magma) I:=[1, 2, 2, 4, 4, 4, 5, 6]; [0] cat [n le 7 select I[n] else Self(n-1) + Self(n-6) - Self(n-7): n in [1..30]]; // G. C. Greubel, Apr 09 2018

Crossrefs

Cf. A296102, A303006, A303053.

Sequence in context: A090557 A230875 A035660 * A115367 A084841 A144202

Adjacent sequences: A302402 A302403 A302404 * A302406 A302407 A302408

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 07 2018

Status

approved