A302404 Total domination number of the n-Moebius ladder.
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
Offset: 0
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).
Programs
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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
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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] -
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
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
Comments