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A302404 Total domination number of the n-Moebius ladder. 2
0, 2, 2, 2, 3, 4, 4, 6, 6, 6, 7, 8, 8, 10, 10, 10, 11, 12, 12, 14, 14, 14, 15, 16, 16, 18, 18, 18, 19, 20, 20, 22, 22, 22, 23, 24, 24, 26, 26, 26, 27, 28, 28, 30, 30, 30, 31, 32, 32, 34, 34, 34, 35, 36, 36, 38, 38, 38, 39, 40, 40, 42, 42, 42, 43, 44, 44, 46, 46, 46, 47 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, Moebius Ladder

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) = (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.

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

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

a(n) = a(n-6) + 4. - Andrew Howroyd, Apr 18 2018

a(n) = a(n-6*k) + 4*k. - Eric W. Weisstein, Apr 23 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, 20}]

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {2, 2, 2, 3, 4, 4, 6}, {0, 50}]

CoefficientList[Series[x (2 + x^3 + x^4)/((-1 + x)^2 (1 + x + x^2 + x^3 + x^4 + x^5)), {x, 0, 20}], x]

PROG

(PARI) x='x+O('x^50); concat(0, Vec(x*(2+x^3+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5)))) \\ G. C. Greubel, Apr 09 2018

(MAGMA) I:=[2, 2, 2, 3, 4, 4, 6]; [0] cat [n le 7 select I[n] else Self(n-1) + Self(n-6) - Self(n-7): n in [1..50]]; // G. C. Greubel, Apr 09 2018

CROSSREFS

Cf. A295420, A302405, A303046, A301337.

Sequence in context: A215473 A071988 A301337 * A029050 A066920 A035381

Adjacent sequences:  A302401 A302402 A302403 * A302405 A302406 A302407

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 07 2018

STATUS

approved

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Last modified September 18 01:54 EDT 2021. Contains 347504 sequences. (Running on oeis4.)