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A068744
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Number of potential flows in 3 X 3 array with integer velocities in -n..n, i.e. number of 3 X 3 arrays with adjacent elements differing by no more than n, counting arrays differing by a constant only once.
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35
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1, 1665, 87825, 1253329, 9230193, 45642289, 172989921, 542131425, 1473095713, 3582226465, 7970825457, 16492629297, 32119620625, 59427841617, 105227044417, 179360179905, 295700892993, 473379359425, 738268965841
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Let y=2*n-1; Then apparently a(n) = y^2*(529*y^6+910*y^4+721*y^2+360)/2520. See A068745 (4 X 4) and A063496 (2 X 2), which is y*(2*y^2+1)/3 under the same transformation. Suggests total degree N X N-1, with a factor y or y^2 to make the remaining polynomial even. - R. H. Hardin (rhhardin(AT)att.net), Jan 02 2007
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CROSSREFS
| 2 X 2 A063496, 4 X 4 A068745, 5 X 5 A068746, 6 X 6 A068747, by velocity limit 1..14 A068748-A068761, solenoidal flows A068722-A068738.
Sequence in context: A163273 A104019 A054810 * A054811 A164773 A054812
Adjacent sequences: A068741 A068742 A068743 * A068745 A068746 A068747
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Feb 27 2002
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