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Search: id:A057566
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| A057566 |
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Number of collinear triples in a 3 X n rectangular grid. |
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+0
1
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| 0, 1, 2, 8, 20, 43, 78, 130, 200, 293, 410, 556, 732, 943, 1190, 1478, 1808, 2185, 2610, 3088, 3620, 4211, 4862, 5578, 6360, 7213, 8138, 9140, 10220, 11383, 12630, 13966, 15392, 16913, 18530, 20248, 22068, 23995, 26030, 28178, 30440, 32821, 35322
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Conjecture: a(n)=5Floor[(2n^3-3n^2-n)/24]+Floor[(2(n-1)^3-3(n-1)^2-(n-1))/24]+n, which fits all of the listed terms.
a(n)=a(n-1)+b(n), with a(0)=-2, b(0)=8 and being b(n)=b(n-1)-7+Sum_{k=0..n}{5*(k mod 2)+[(k+1) mod 2]} - Paolo P. Lava (ppl(AT)spl.at), Aug 24 2007
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MAPLE
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P:=proc(n) local a, b, i; b:=8; a:=-2; for i from 0 by 1 to n do b:=b-7+sum('(5*(k mod 2)+((k+1) mod 2))', 'k'=0..i); a:=a+b; print(a); od; end: P(200); - Paolo P. Lava (ppl(AT)spl.at), Aug 24 2007
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CROSSREFS
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Second differences give A047264. Third differences are periodic {5, 1, 5, 1, ...} and form A010686. See A000938 for the n X n grid.
Sequence in context: A058037 A048096 A072250 this_sequence A009303 A096586 A165751
Adjacent sequences: A057563 A057564 A057565 this_sequence A057567 A057568 A057569
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Oct 04 2000
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