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A211783
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Rectangular array: R(n,k)=n^2+[(n^2)/2]+...+[(n^2)/k], where [ ]=floor, by antidiagonals.
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1
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1, 4, 1, 9, 6, 1, 16, 13, 7, 1, 25, 24, 16, 8, 1, 36, 37, 29, 18, 8, 1, 49, 54, 45, 33, 19, 8, 1, 64, 73, 66, 51, 36, 20, 8, 1, 81, 96, 89, 75, 56, 38, 21, 8, 1, 100, 121, 117, 101, 82, 60, 40, 22, 8, 1, 121, 150, 148, 133, 110, 88, 63, 42, 23, 8, 1, 144, 181, 183
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OFFSET
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0,2
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COMMENTS
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For n>=1, row n is a homogeneous linear recurrence sequence with palindromic recurrence coefficients in the sense described at A211701.
The sequence approached as a limit of the rows is A175346: (1,8,23,50,87,140,...)
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LINKS
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EXAMPLE
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Northwest corner:
1....4....9....16....25....36
1....6....13...24....37....54
1....7....16...29....35....66
1....8....18...33....51....75
1....8....19...36....56....82
1....8....20...38....60....88
1....8....21...40....63....93
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MATHEMATICA
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f[n_, m_] := Sum[Floor[n^2/k], {k, 1, m}]
TableForm[Table[f[n, m], {m, 1, 40}, {n, 1, 16}]]
Flatten[Table[f[n + 1 - m, m], {n, 1, 14}, {m, 1, n}]]
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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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