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A232441
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Sequence read from antidiagonals of rectangular array given by A(n,k) = 2^(2*k)*(Sum_{j=1..n-floor(n/2)-1} (cos(j*Pi/n))^(2*k)), rows n >= 3, columns k >= 0.
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1
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1, 1, 1, 2, 2, 1, 2, 3, 4, 1, 3, 4, 7, 8, 1, 3, 5, 10, 18, 16, 1, 4, 6, 13, 28, 47, 32, 1, 4, 7, 16, 38, 82, 123, 64, 1, 5, 8, 19, 48, 117, 244, 322, 128, 1, 5, 9, 22, 58, 152, 370, 730, 843, 256, 1, 6, 10, 25, 68
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OFFSET
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3,4
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COMMENTS
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Row indices n begin with 3, column indices k begin with 0.
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LINKS
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FORMULA
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A(2*m+1,k) = A186740(m,k), m = 1,2,....
Conjecture: A(n,k) = floor(A198632(n-1,k)/2), n >= 3, k >= 0.
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EXAMPLE
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...
2, 3, 7, 18, 47, 123, 322, 843, 2207, 5778,15127,...
2, 4, 10, 28, 82, 244, 730, 2188, 6562,19684,59050,...
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MATHEMATICA
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Table[Function[m, FullSimplify[2^(2 k)*Sum[Cos[j*Pi/m]^(2 k), {j, m - Floor[m/2] - 1}]]][n - k + 1], {n, 3, 12}, {k, 0, n - 2}] // Flatten (* Michael De Vlieger, Mar 18 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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