

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
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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, blowingup, 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. 701728


FORMULA

Triangle is divided by 2^(6n) 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



