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A144469 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}. 0
102, 51, 51, 23, 28, 23, 12, 14, 14, 12, 3, 4, 8, 4, 3, 1, 2, 4, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are: {102, 102, 74, 52, 22, 14}.

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.

LINKS

Table of n, a(n) for n=1..21.

Andrew Bashelor, Amy Ksir, and Will Traves, Enumerative Algebraic Geometry of Conics, The American Mathematical Monthly, vol. 115, no. 8, October 2008, pp. 701-728

FORMULA

Triangle is divided by 2^(6-n) by levels.

EXAMPLE

{{102},

{51, 51},

{23, 28, 23},

{12, 14, 14, 12},

{3, 4, 8, 4, 3},

{1, 2, 4, 4, 2, 1}}

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]}];

CROSSREFS

Sequence in context: A204749 A244949 A266017 * A009101 A031962 A303504

Adjacent sequences:  A144466 A144467 A144468 * A144470 A144471 A144472

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 09 2008

STATUS

approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)