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A133357
Number of 2-colorings of a 3 X n rectangle for which no subsquare has monochromatic corners.
4
1, 8, 50, 276, 1498, 8352, 46730, 260204, 1447890, 8062968, 44907298, 250082756, 1392637914, 7755351712, 43188407610, 240509081468, 1339353796226, 7458635202952, 41535888495186, 231306378487028, 1288106280145770, 7173247100732400, 39946606186601514
OFFSET
0,2
COMMENTS
Figures obtained via clever exhaustion, using Gray Codes.
REFERENCES
J. Solymosi, "A Note on a Question of Erdos and Graham", Combinatorics, Probability and Computing, Volume 13, Issue 2 (March 2004) 263 - 267.
FORMULA
G.f.: -(x+1)*(8*x^7-12*x^6-2*x^5-16*x^4-30*x^3-15*x^2-4*x-1) / (24*x^8-4*x^7-46*x^6-66*x^5-74*x^4-25*x^3-7*x^2-3*x+1). - Alois P. Heinz, Feb 18 2015
EXAMPLE
a(1) = 8, because there are no conditions.
a(2) = 50 because if the middle row is not monochromatic, the top and bottom rows are unconstrained, contributing 2*4*4. If the middle row is monochromatic, the top and bottom rows can each take on only 3 values contributing 2*3*3.
MAPLE
gf:= -(x+1)*(8*x^7-12*x^6-2*x^5-16*x^4-30*x^3-15*x^2-4*x-1)/
(24*x^8-4*x^7-46*x^6-66*x^5-74*x^4-25*x^3-7*x^2-3*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30); # Alois P. Heinz, Feb 18 2015
CROSSREFS
Column k=3 of A255256.
Sequence in context: A163228 A033463 A030279 * A081675 A283277 A081180
KEYWORD
nonn,easy
AUTHOR
Victor S. Miller, Dec 21 2007
EXTENSIONS
a(0), a(8)-a(22) from Alois P. Heinz, Feb 18 2015
STATUS
approved