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A144469
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Triangle from Steiner's problem: {3264}, {816, 816}, {184, 224, 184}, {48, 56, 56, 48}, {6, 8, 16, 8, 6}, {1, 2, 4, 4, 2, 1}.
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0
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102, 51, 51, 23, 28, 23, 12, 14, 14, 12, 3, 4, 8, 4, 3, 1, 2, 4, 4, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:
{102, 102, 74, 52, 22, 14}.
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REFERENCES
| http://www.maa.org/pubs/monthly_oct08_toc.html, Enumerative Algebraic Geometry of Conics By: Andrew Bashelor, Amy Ksir and Will Traves andrew.bashelor(AT)mac.com, ksir(AT)usna.edu, traves(AT)usna.edu A recent undergraduate project dealt with Steiner's problem: How many conics are simultaneously tangent to five fixed conics? This challenging problem can be solved by first tackling a collection of easier enumerative problems involving conics, lines and points. Many beautiful ideas in algebraic geometry make an appearance along the way. Complicated tools like moduli spaces, blowing-up, duality and cohomology are both natural and accessible when studied in this context. A list of fun problems develops connections to other topics, such as string theory and kissing spheres.
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FORMULA
| Triangle is divided by 2^(6-n) by levels.
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EXAMPLE
| {{102},
{51, 51},
{23, 28, 23},
{12, 14, 14, 12},
{3, 4, 8, 4, 3},
{1, 2, 4, 4, 2, 1}}
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MATHEMATICA
| a = {{102}, {51, 51}, {23, 28, 23}, {12, 14, 14, 12}, {3, 4, 8, 4, 3}, {1, 2, 4, 4, 2, 1}}; Flatten[a] Table[Sum[a[[n]][[m]], {m, 1, n}], {n, 1, Length[a]}]; Table[2^(6 - n)*Table[a[[n]][[m]], {m, 1, n}], {n, 1, Length[a]}];
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CROSSREFS
| Sequence in context: A006064 A015164 A204749 * A009101 A031962 A135601
Adjacent sequences: A144466 A144467 A144468 * A144470 A144471 A144472
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 09 2008
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