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A302406 Total domination number of the n X n torus grid graph. 3
0, 1, 2, 3, 4, 8, 10, 14, 16, 23, 26, 33, 36, 46, 50, 60, 64, 77, 82, 95, 100, 116, 122, 138, 144, 163, 170, 189, 196, 218, 226, 248, 256, 281, 290, 315, 324, 352, 362, 390, 400, 431, 442, 473, 484, 518, 530, 564, 576, 613, 626, 663, 676, 716, 730, 770, 784, 827, 842, 885 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..59.

Eric Weisstein's World of Mathematics, Torus Grid Graph

Eric Weisstein's World of Mathematics, Total Domination Number

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

FORMULA

a(n) = (3 -(-1)^n*(n - 1) + n + 2*n^2 - 4*cos(n*Pi/2) + 2*sin(n*Pi/2))/8.

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7).

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

a(n) ~ n^2/4. - Andrew Howroyd, Apr 21 2018

MATHEMATICA

Table[(3-(-1)^n*(n-1)+n+2*n^2-4*Cos[n*Pi/2]+2*Sin[n*Pi/2])/8, {n, 0, 20}]

LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {1, 2, 3, 4, 8, 10, 14}, {0, 20}]

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

PROG

(PARI) for(n=0, 30, print1(round((3-(-1)^n*(n-1) +n +2*n^2 -4*cos(n*Pi/2) + 2*sin(n*Pi/2))/8), ", ")) \\ G. C. Greubel, Apr 09 2018

(MAGMA) R:=RealField(); [Round((3 -(-1)^n*(n-1) +n +2*n^2 - 4*Cos(n*Pi(R)/2) + 2*Sin(n*Pi(R)/2))/8): n in [0..20]]; // G. C. Greubel, Apr 09 2018

CROSSREFS

Cf. A303210, A303213.

Sequence in context: A222264 A051783 A033083 * A328092 A242762 A005542

Adjacent sequences:  A302403 A302404 A302405 * A302407 A302408 A302409

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 07 2018

STATUS

approved

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Last modified August 11 14:49 EDT 2022. Contains 356066 sequences. (Running on oeis4.)