A348863 Triangle T(n, k) is the number of times 2^k*3^(-n) arises in the n-th partition appearing in an iterated sequence of partitions of 1 (one for each integer n) into numbers of the form 2^k*3^(-n), for n>=0, read by rows.

1, 1, 1, 3, 1, 1, 7, 6, 0, 1, 21, 16, 3, 0, 1, 57, 51, 13, 0, 0, 1, 171, 149, 39, 5, 0, 0, 1, 499, 454, 117, 23, 0, 0, 0, 1, 1497, 1348, 360, 66, 9, 0, 0, 0, 1, 4449, 4083, 1061, 207, 41, 0, 0, 0, 0, 1, 13347, 12191, 3252, 591, 126, 17, 0, 0, 0, 0, 1, 39927, 36658, 9738, 1799, 370, 81, 0, 0, 0, 0, 0, 1

Offset

0,4

Comments

See Calegari link for details.

Links

Table of n, a(n) for n=0..77.

Danny Calegari, Sausages and Butcher Paper, arXiv:2105.11265 [math.DS], 2021.

Danny Calegari, Combinatorics of the Tautological Lamination, arXiv:2106.00578 [math.DS], 2021.

Example

Triangle begins:
  1;
  1, 1;
  3, 1, 1;
  7, 6, 0, 1;
  21, 16, 3, 0, 1;
  57, 51, 13, 0, 0, 1;
  171, 149, 39, 5, 0, 0, 1;
  ...

Crossrefs

Sequence in context: A287213 A284631 A154341 * A202181 A130749 A250118

Adjacent sequences: A348860 A348861 A348862 * A348864 A348865 A348866

Keyword

nonn,tabl

Author

Michel Marcus, Nov 02 2021

Status

approved