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A165394
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Number of slanted 2 X n (i=1..2) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 3 neighbors with the same value.
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1
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1, 9, 37, 105, 241, 481, 869, 1457, 2305, 3481, 5061, 7129, 9777, 13105, 17221, 22241, 28289, 35497, 44005, 53961, 65521, 78849, 94117, 111505, 131201, 153401, 178309, 206137, 237105, 271441, 309381, 351169, 397057, 447305, 502181, 561961, 626929
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OFFSET
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2,2
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LINKS
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FORMULA
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Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>=7.
G.f.: x^2*(1 + x)*(1 + 3*x - x^2 + x^3) / (1 - x)^5.
a(n) = (15 - 20*n + 11*n^2 - 4*n^3 + n^4) / 3.
(End)
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EXAMPLE
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Some solutions for n=6:
...1.1.2.2.2.2.....1.3.3.3.2.2.....1.1.1.1.1.2.....1.1.3.2.2.2..
.....3.3.4.4.4.4.....3.3.3.2.4.4.....3.3.2.2.2.4.....3.3.2.2.2.4
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...1.1.1.2.2.2.....1.1.1.3.3.2.....1.3.3.3.2.2.....1.1.1.2.2.2..
.....3.1.1.4.4.4.....3.3.3.3.2.4.....3.3.3.3.2.4.....3.1.2.2.2.4
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...1.1.1.1.4.2.....1.1.2.2.2.2.....1.3.2.2.2.2.....1.3.2.2.2.2..
.....3.3.4.4.4.4.....3.2.2.4.4.4.....3.3.3.3.4.4.....3.3.3.2.2.4
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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