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A114327
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Table T(n,m) = n-m read by antidiagonals.
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4
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0, 1, -1, 2, 0, -2, 3, 1, -1, -3, 4, 2, 0, -2, -4, 5, 3, 1, -1, -3, -5, 6, 4, 2, 0, -2, -4, -6, 7, 5, 3, 1, -1, -3, -5, -7, 8, 6, 4, 2, 0, -2, -4, -6, -8, 9, 7, 5, 3, 1, -1, -3, -5, -7, -9, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, 11, 9, 7, 5, 3, 1, -1, -3, -5, -7, -9, -11, 12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Contribution from Clark Kimberling, May 31 2011: (Start)
If we arrange A000027 as an array with northwest corner
1....2....4....7.....17...
3....5....8....12....18...
6....9....13...18....24...
10...14...19...25....32...
diagonals can be numbered as follows depending on their distance to the main diagonal:
Diag 0: 1,5,13,25,...
Diag 1: 2,8,18,32,...
Diag -1: 3,9,19,33,...,
Then a(n) in the flattend array is the number of the diagonal that contains n+1. (End)
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FORMULA
| G.f. (x-y)/((1-x)^2(1-y)^2)). E.g.f. sum T(n,m)x^n/n!y^m/m! = (x-y)e^{x+y}. a(n) = A002262(n) - A025581(n).
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EXAMPLE
| Top left corner of table:
0 1 2 ...
-1 0 1 ...
-2 -1 0 ...
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CROSSREFS
| Apart from signs, same as A049581. Cf. A003056, A025581, A002262.
Sequence in context: A105805 A194547 A049581 * A073450 A071447 A063514
Adjacent sequences: A114324 A114325 A114326 * A114328 A114329 A114330
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KEYWORD
| easy,sign,tabl,nice
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006
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