A144469 Finite table read by antidiagonals: T(n, m) is the number of conics passing through n points, tangent to m lines, and tangent to k=5-n-m conics in general position, divided by 2^k, with 0 <= n+m <= 5.

102, 51, 51, 23, 28, 23, 12, 14, 14, 12, 3, 4, 8, 4, 3, 1, 2, 4, 4, 2, 1

Offset

1,1

Comments

Row (i. e. antidiagonal) sums are: {102, 102, 74, 52, 22, 14}.

T(0, 0) * 2^5 = A328148(2) = 3264 answers the Steiner's problem: How many conics are simultaneously tangent to five fixed conics?

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.

Example

The complete triangle:
{{102},
{51, 51},
{23, 28, 23},
{12, 14, 14, 12},
{3, 4, 8, 4, 3},
{1, 2, 4, 4, 2, 1}}
Without dividing by 2^k, the triangle becomes:
{3264}
{816, 816}
{184, 224, 184}
{48, 56, 56, 48}
{6, 8, 16, 8, 6}
{1, 2, 4, 4, 2, 1}

Crossrefs

Cf. A328148.

Sequence in context: A204749 A244949 A266017 * A009101 A031962 A303504

Adjacent sequences: A144466 A144467 A144468 * A144470 A144471 A144472

Keyword

nonn,tabl,fini,full

Author

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

Extensions

Edited by Andrey Zabolotskiy, Jun 14 2022

Status

approved