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A138099
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Irregular triangle read by rows: T(n,k) = k + floor(n/2), 1 <= k <= ceiling(n/2).
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6
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1, 2, 2, 3, 3, 4, 3, 4, 5, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11, 12, 13, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 15, 9, 10, 11, 12, 13, 14, 15, 16, 9, 10, 11, 12, 13
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OFFSET
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1,2
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COMMENTS
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Previous name was: Base for 8 X 32 Janet periodic table of elements. Ordered energy levels of atoms.
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LINKS
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FORMULA
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a(n) = n - floor((1/4)*(floor(sqrt(4*n-3))-1)^2). - Mircea Merca, Feb 05 2012
Conjecture: a(n) = HookSum(T(n))-HookSum(T(n-1)), where HookSum(A) is the sum of all hooks across a tableau A, and T(n) are the spiraling sequence of tableaux:
o oo ooo
Empty, o, oo, oo, oo, oo , ooo , ooo, ooo, ooo, ...
o oo ooo ooo ooo ooo ooo
(End)
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EXAMPLE
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Triangle begins:
1;
2;
2, 3;
3, 4;
3, 4, 5;
4, 5, 6;
4, 5, 6, 7;
5, 6, 7, 8;
...
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MATHEMATICA
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Table[k+Floor[n/2], {n, 20}, {k, Ceiling[n/2]}]//Flatten (* Harvey P. Dale, Aug 15 2017 *)
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PROG
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(Magma) lst:=[]; for n in [1..16] do for k in [1..Ceiling(n/2)] do Append(~lst, k+Floor(n/2)); end for; end for; lst; // Arkadiusz Wesolowski, Jun 15 2014
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CROSSREFS
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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