A055907 Triangle: number of directed site animals on hexagonal net (honeycomb) with n total sites and k sites supported in one particular way.

0, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 6, 10, 6, 1, 1, 9, 21, 20, 8, 1, 1, 12, 39, 53, 36, 10, 1, 1, 16, 67, 121, 128, 56, 12, 1, 1, 20, 107, 249, 388, 240, 74, 14, 1, 1, 25, 163, 471, 1050, 854, 331, 100, 16, 1, 1, 30, 238, 836, 2601, 2654, 1212, 511, 130, 18, 1, 1, 36, 337

Offset

0,5

Links

Table of n, a(n) for n=0..68.

A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189 (A_h of Section 6).

A. J. Guttmann and A. R. Conway, Hexagonal lattice directed site animals, Statistical Physics on the Eve of the Twenty-First Century, ed. M. T. Batchelor, World Scientific, 1999 (F_h of Section 4).

Example

Table begins:
  0;
  1,  1;
  1,  2,  1;
  1,  4,  4,  1;
  1,  6, 10,  6,  1;
  ...

Crossrefs

Row sums give A055919.

Columns 1-9 give: A002620(n+1), A055908, A055909, A055910, A055911, A055912, A055913, A055914, A055915.

Cf. A055898.

Sequence in context: A157528 A132731 A128966 * A259698 A274643 A172991

Adjacent sequences: A055904 A055905 A055906 * A055908 A055909 A055910

Keyword

nonn,tabl

Author

Christian G. Bower, Jun 14 2000

Extensions

Name edited by Andrey Zabolotskiy, Jun 21 2022

Status

approved