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Search: id:A098737
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| A098737 |
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Triangle read by rows: number of triangles formed by lines from two vertices of a triangle to the opposite side that segment the opposite sides into m and n segments. Since f(m,n) = f(n,m), it suffices to give the results in a triangular table. |
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+0
2
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| 1, 3, 8, 6, 15, 27, 10, 24, 42, 64, 15, 35, 60, 90, 125, 21, 48, 81, 120, 165, 216, 28, 63, 105, 154, 210, 273, 343, 36, 80, 132, 192, 260, 336, 420, 512, 45, 99, 162, 234, 315, 405, 504, 612, 729, 55, 120, 195, 280, 375, 480, 595, 720, 855, 1000, 66, 143, 231, 330
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Frank Buss gave this as a puzzle; K. L. Metlov solved it, submitting his result in the J language created by Kenneth Iverson. The program given below is only five tokens long. J defines a series of three functions to be a "fork" defined by x (f g h ) y = (x f y) g (f h y) - a generalization of the usual mathematical practice of writing (f + g) y to mean (f y) + (g y). J also has a primitive "half" and has a dummy function "cap" whose purpose is to permit more forks to be written. 3 (* * +) 5 is thus (3 * 5) * (3 + 5) or 120. cap half 3 (* * +) 5 is thus 60.
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FORMULA
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f(m, n) = 1/2 * (m * n) * (m + n)
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EXAMPLE
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f(3,5) is 60, from 1/2 * (3 * 5) * (3 + 5) or 1/2 * 15 * 8.
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MATHEMATICA
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t[m_, n_] := (m*n)(m + n)/2; Flatten[ Table[ t[m, n], {m, 10}, {n, m}]] (from Robert G. Wilson v Nov 04 2004)
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PROGRAM
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(J language) cap half * * +
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CROSSREFS
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Sequence in context: A021725 A080939 A155724 this_sequence A164654 A072396 A001175
Adjacent sequences: A098734 A098735 A098736 this_sequence A098738 A098739 A098740
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Eugene McDonnell (eemcd(AT)mac.com), Oct 29 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2004
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