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A302255 Total domination number of the n-antiprism graph. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A102548 A004001

Adjacent sequences:  A302252 A302253 A302254 * A302256 A302257 A302258

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 07 2018

STATUS

approved

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Last modified June 19 12:57 EDT 2019. Contains 324222 sequences. (Running on oeis4.)