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Search: id:A068745
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| A068745 |
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Number of potential flows in 4 X 4 array with integer velocities in -n..n, i.e. number of 4 X 4 arrays with adjacent elements differing by no more than n, counting arrays differing by a constant only once. |
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22
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| 1, 690437, 1133641543, 164185416899, 6913624013061, 138190481342321, 1678843050246451, 14285299502131463, 93044501704039945, 492225938556374973, 2204710243834695807, 8617480381892283531
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Let y=2*n-1; it appears that a(n) = y*(2623243666*y^14 + 9598591135*y^12 + 17180805187*y^10 + 20342655905*y^8 + 17636121503*y^6 + 10907793260*y^4 + 3135618144*y^2 + 304819200)/81729648000. - Ron Hardin (rhhardin(AT)att.net), Jan 01 2007
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CROSSREFS
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2 X 2 A063496, 3 X 3 A068744, 5 X 5 A068746, 6x6 A068747, by velocity limit 1..14 A068748-A068761, solenoidal flows A068722-A068738.
Cf. 4 X 4 this sequence (degree 4*4-1) with factor 2n-1 ; 3 X 3 A068744 (degree 3*3-1) with factor (2n-1)^2 ; 2 X 2 A063496 (degree 2*2-1) with factor 2n-1.
Sequence in context: A010095 A081415 A101698 this_sequence A010084 A114676 A027829
Adjacent sequences: A068742 A068743 A068744 this_sequence A068746 A068747 A068748
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KEYWORD
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nonn
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AUTHOR
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Ron Hardin (rhhardin(AT)att.net), Feb 27 2002
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