A302488 Total domination number of the n X n grid graph.

1, 2, 3, 6, 9, 12, 15, 20, 25, 30, 35, 42, 49, 56, 63, 72, 81, 90, 99, 110, 121, 132, 143, 156, 169, 182, 195, 210, 225, 240, 255, 272, 289, 306, 323, 342, 361, 380, 399, 420, 441, 462, 483, 506, 529, 552, 575, 600, 625, 650, 675, 702, 729, 756, 783, 812, 841, 870, 899, 930

Offset

2,2

Comments

Extended to a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=2..61.

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Total Domination Number

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Formula

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

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

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

Mathematica

Table[(-1 + (-1)^n + 2 n (2 + n) + 4 Sin[n Pi/2])/8, {n, 20}]
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 2, 3, 6, 9, 12}, 20]
CoefficientList[Series[(-1 - 2 x^3 + x^4)/((-1 + x)^3 (1 + x + x^2 + x^3)), {x, 0, 20}], x]

Prog

(PARI) for(n=1, 30, print1(round(((-1)^n + 2*n*(n + 2) + 4*sin(n*Pi/2) - 1)/8), ", ")) \\ G. C. Greubel, Apr 09 2018
(Magma) R:=RealField(); [Round(((-1)^n + 2*n*(n + 2) + 4*Sin(n*Pi(R)/2) - 1)/8): n in [1..30]]; // G. C. Greubel, Apr 09 2018

Crossrefs

Main diagonal of A300358.

Cf. A303142.

Sequence in context: A145441 A308012 A077121 * A348448 A140495 A174873

Adjacent sequences: A302485 A302486 A302487 * A302489 A302490 A302491

Keyword

nonn

Author

Eric W. Weisstein, Apr 08 2018

Status

approved