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A302488
Total domination number of the n X n grid graph.
4
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
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Total Domination Number
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 08 2018
STATUS
approved