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A120413
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Largest even number strictly less than n^2.
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1
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0, 2, 8, 14, 24, 34, 48, 62, 80, 98, 120, 142, 168, 194, 224, 254, 288, 322, 360, 398, 440, 482, 528, 574, 624, 674, 728, 782, 840, 898, 960, 1022, 1088, 1154, 1224, 1294, 1368, 1442, 1520, 1598, 1680, 1762, 1848, 1934, 2024, 2114, 2208, 2302, 2400, 2498, 2600
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OFFSET
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1,2
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COMMENTS
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Longest non-intersecting route from (0, 0) to (n - 1, n - 1) staying in an (n - 1) X (n - 1) box (shortest route is length 2n A005843).
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LINKS
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FORMULA
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a(n) = (-1 + (-1)^n + 4*n + 2*n^2)/2.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: 2*x*(1 + 2*x - x^2)/((1-x)^3*(1+x)). (End)
a(n) = n^2 - 2 for even n; a(n) = n^2 - 1 for odd n. -Dennis P. Walsh, Apr 15 2016
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MAPLE
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seq(2*ceil(n^2/2)-2, n=1..50);
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MATHEMATICA
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Flatten[Table[{(2n - 1)^2 - 1, 4n^2 - 2}, {n, 25}]] (* Alonso del Arte, Apr 15 2016 *)
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PROG
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(PARI) lista(nn) = for(n=0, nn, print1((-1+(-1)^n+4*n+2*n^2)/2, ", ")); \\ Altug Alkan, Apr 15 2016
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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