A302255 Total domination number of the n-antiprism graph.

0, 1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 31, 32, 32, 32, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 40, 40, 41

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..71.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Total Domination Number

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

Formula

a(n) = a(n-1) + a(n-7) - a(n-8).

G.f.: x*(1 + x + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = a(n-7) + 4. - Andrew Howroyd, Apr 18 2018

a(n) = a(n-7*k) + 4*k. - Eric W. Weisstein, Apr 19 2018

Mathematica

Table[(4 + 4 n + E^(4 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 1] + E^(-4 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 2] + E^(-2 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 3] + E^(2 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 4] + E^(-6 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 5] + E^(6 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 6])/ 7, {n, 20}] // RootReduce
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 2, 3, 4, 4, 4, 5, 6, 6}, {0, 20}]
CoefficientList[Series[x (1 + x + x^3 + x^4)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 20}], x]

Prog

(PARI) x='x+O('x^50); concat(0, Vec(x*(1+x+x^3+x^4)/((1-x)^2*(1+x+x^2+ x^3+x^4+x^5+x^6)))) \\ G. C. Greubel, Apr 09 2018
(Magma) I:=[2, 2, 3, 4, 4, 4, 5, 6]; [0, 1] cat [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..30]]; // G. C. Greubel, Apr 09 2018

Crossrefs

Cf. A302652, A302760, A302763.

Sequence in context: A307482 A046699 A239105 * A218446 A362965 A102548

Adjacent sequences: A302252 A302253 A302254 * A302256 A302257 A302258

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 07 2018

Status

approved