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A321684 Independent domination number of the n X n grid graph. 2
0, 1, 2, 3, 4, 7, 10, 12, 16, 21, 24, 30, 35, 40, 47, 53, 60, 68, 76, 84, 92, 101, 111, 121, 131, 141, 152, 164, 176, 188, 200, 213, 227, 241, 255, 269, 284, 300, 316, 332, 348, 365, 383, 401, 419, 437, 456, 476, 496, 516, 536, 557, 579, 601, 623, 645, 668 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Simon Crevals, Patric R. J. Östergård, Independent domination of grids, Discrete Math., 338 (2015), 1379-1384.

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

FORMULA

For n >= 14, a(n) = floor((n+2)^2 / 5 - 4).

a(n) = A104519(n+2), the domination number of the n X n grid graph, for all n except for n = 9, 11.

From Colin Barker, Jan 14 2019: (Start)

G.f.: x*(1 + 2*x^4 - x^5 - x^6 + 2*x^7 + x^8 - 4*x^9 + 3*x^10 - 2*x^12 + x^13 + x^14 - 2*x^15 + 2*x^16 - 2*x^18 + x^19) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).

a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n > 20.

(End)

MAPLE

ogf := (-41*x^6 + 47*x^5 - x^3 - x^2 + 41*x - 47)/((x - 1)^3*(x^4 + x^3 + x^2 + x + 1)): ser := series(ogf, x, 44):

(0, 1, 2, 3, 4, 7, 10, 12, 16, 21, 24, 30, 35, 40), seq(coeff(ser, x, n), n=0..42); # Peter Luschny, Jan 14 2019

PROG

(PARI) concat(0, Vec(x*(1 + 2*x^4 - x^5 - x^6 + 2*x^7 + x^8 - 4*x^9 + 3*x^10 - 2*x^12 + x^13 + x^14 - 2*x^15 + 2*x^16 - 2*x^18 + x^19) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Jan 14 2019

CROSSREFS

Cf. A104519, A075324, A299029, A279404, A291297.

Sequence in context: A135419 A051914 A104519 * A117220 A118426 A082008

Adjacent sequences:  A321681 A321682 A321683 * A321685 A321686 A321687

KEYWORD

nonn,easy

AUTHOR

Andrey Zabolotskiy, Jan 14 2019

STATUS

approved

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Last modified November 30 18:46 EST 2021. Contains 349424 sequences. (Running on oeis4.)