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Search: id:A068722
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| A068722 |
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Number of solenoidal flows (flow in = flow out) in a 3 X 3 square array with integer velocities -n .. n. |
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+0
35
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| 1, 35, 247, 925, 2501, 5551, 10795, 19097, 31465, 49051, 73151, 105205, 146797, 199655, 265651, 346801, 445265, 563347, 703495, 868301, 1060501, 1282975, 1538747, 1830985, 2163001, 2538251, 2960335, 3432997, 3960125, 4545751
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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(1-2n+3n^2) * (1-3n+2n^2).
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EXAMPLE
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Sample flows (. represents a space):
Numbers in long rows are on cell walls showing velocity rightward.
Numbers in long columns are on cell floors showing velocity downwards.
3 X 3 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0
.0. -1. -1 . 0
.. 1 . 0. -1
.0 . 0 . 0 . 0
.. 1 . 0. -1
.0 . 1 . 1 . 0
.. 0 . 0 . 0
n=2:
.. 0 . 0 . 0
.0. -2. -1 . 0
.. 2. -1. -1
.0 . 0. -1 . 0
.. 2 . 0. -2
.0 . 2 . 2 . 0
.. 0 . 0 . 0
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CROSSREFS
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Cf. 2 X 2=1, 3, 5, 7..., 4 X 4 A068723, 5 X 5 A068724, 6x6 A068725, by velocity limit 1..13 A068726-A068738.
Adjacent sequences: A068719 A068720 A068721 this_sequence A068723 A068724 A068725
Sequence in context: A064013 A020262 A104474 this_sequence A113941 A067238 A090646
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KEYWORD
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nonn
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AUTHOR
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Ron Hardin (rhh(AT)cadence.com), Feb 26 2002
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