1,1

Row sums are:

{102, 102, 74, 52, 22, 14}.

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.

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

{{102},

{51, 51},

{23, 28, 23},

{12, 14, 14, 12},

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

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

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]}];

Sequence in context: A138720 A006064 A015164 this_sequence A009101 A031962 A135601

Adjacent sequences: A144466 A144467 A144468 this_sequence A144470 A144471 A144472

nonn,uned

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 09 2008