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Search: id:A126587
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| A126587 |
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a(n) = number of integer lattice points inside the right-angle triangle with legs 3n and 4n (and hypotenuse 5n). |
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+0
1
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| 3, 17, 43, 81, 131, 193, 267, 353, 451, 561, 683, 817, 963, 1121, 1291, 1473, 1667, 1873, 2091, 2321, 2563, 2817, 3083, 3361, 3651, 3953, 4267, 4593, 4931, 5281, 5643, 6017, 6403, 6801, 7211, 7633, 8067, 8513, 8971, 9441, 9923, 10417, 10923, 11441
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Zak Seidov, Inside Points".
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FORMULA
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By Pick's theorem, a(n) = 6n^2 - 4n + 1. - Nick Hobson (nickh(AT)qbyte.org), Mar 13 2007
O.g.f.: -x*(3+8*x+x^2)/(-1+x)^3 = -1-12/(-1+x)^3-11/(-1+x)-22/(-1+x)^2 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 10 2007
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EXAMPLE
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At n=1, three lattice points (1,1), (1,2) and (2,1) are inside the triangle with vertices at the points (0,0), (3n,0) and (0,4n); hence a(1)=3.
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MATHEMATICA
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nip[a_, b_]:=Sum[Floor[b-b*i/a-10^-6], {i, a-1}] Table[nip[3k, 4k], {k, 100}]
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CROSSREFS
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Sequence in context: A049078 A135471 A092347 this_sequence A108126 A106256 A091624
Adjacent sequences: A126584 A126585 A126586 this_sequence A126588 A126589 A126590
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)gmail.com), Jan 05 2007
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