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A049695
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Array T read by diagonals; T(i,j)=number of nonnegative slopes of lines determined by 2 lattice points in [ 0,i ] X [ 0,j ] if i>0; T(0,j)=1 if j>0; T(0,0)=0.
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7
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0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 4, 1, 1, 5, 6, 6, 5, 1, 1, 6, 7, 8, 7, 6, 1, 1, 7, 9, 10, 10, 9, 7, 1, 1, 8, 10, 13, 12, 13, 10, 8, 1, 1, 9, 12, 14, 16, 16, 14, 12, 9, 1, 1, 10, 13, 17, 17, 20, 17, 17, 13, 10, 1, 1, 11, 15, 19, 21, 22, 22, 21, 19, 15, 11, 1, 1, 12, 16, 21, 23, 27, 24, 27
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The infinity slope is not counted unless i=0 and j>0. [From Max Alekseyev (maxale(AT)gmail.com), Oct 23 2008]
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LINKS
| Max A. Alekseyev. On the number of two-dimensional threshold functions. SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184
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FORMULA
| For m,n>0, T(m,n) = 1 + U(m,n) = 1 + SUM[i=1..m,j=1..n,gcd(i,j)=1] 1. [From Max Alekseyev (maxale(AT)gmail.com), Oct 23 2008]
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EXAMPLE
| Diagonals (each starting on row 1): {0}; {1,1}; {1,2,1}; ...
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CROSSREFS
| Cf. A005598, A049703.
Cf. A114043. [From Max Alekseyev (maxale(AT)gmail.com), Oct 23 2008]
Sequence in context: A192650 A178059 A116188 * A096589 A176427 A099573
Adjacent sequences: A049692 A049693 A049694 * A049696 A049697 A049698
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms and formula from Max Alekseyev (maxale(AT)gmail.com), Oct 23 2008
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