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A090767
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Numbers of the form 3xyz + 2(xy + yz + zx) + (x + y + z) for x, y, z positive integers.
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1
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12, 20, 28, 33, 36, 44, 46, 52, 54, 59, 60, 64, 68, 72, 75, 76, 82, 84, 85, 92, 96, 98, 100, 104, 105, 108, 111, 116, 117, 118, 124, 128, 132, 133, 136, 137, 138, 140, 144, 148, 150, 151, 154, 156, 159, 162, 163, 164, 170, 172, 174, 176, 180, 184, 188, 189, 190
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is the set of numbers which count the unit sticks or unit segments needed to construct a three-dimensional cubic lattice made up from unit cubes. This generalizes the two-dimensional version which is A047845 (numbers of the form 2xy+x+y for x and y positive integers) and is also the numbers of sticks needed to construct a rectangular lattice of unit squares.
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EXAMPLE
| a(1) = 12 because there are 12 edges to a cube.
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MAPLE
| SeqGen1 := proc(n, N) local a, b, c, F, V, v; # n specifies the search space; N specifies the maximal number to appear in the initial segment of the sequence F := 3*x*y*z + 2*(x*y+y*z+z*x)+x+y+z; V := {}; for a from 1 to n do for b from1 to n do for c from b to n do v := subs(x=a, y=b, F); if v < N then V := V union {v}; fi; od; od; sort(V) end:
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CROSSREFS
| Cf. A047845.
Sequence in context: A035511 A095035 A108027 * A117227 A110187 A096156
Adjacent sequences: A090764 A090765 A090766 * A090768 A090769 A090770
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KEYWORD
| nonn
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AUTHOR
| John Mason (j.h.mason(AT)open.ac.uk), Feb 02 2004
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 04 2004
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