A250485 Regular triangle array: number of [0-r]-covering hierarchies with thickness = e.

1, 1, 2, 1, 6, 4, 1, 14, 22, 8, 1, 30, 86, 64, 16, 1, 62, 294, 346, 168, 32, 1, 126, 938, 1594, 1140, 416, 64, 1, 254, 2874, 6746, 6422, 3376, 992, 128, 1, 510, 8586, 27098, 32758, 22192, 9344, 2304, 256, 1, 1022, 25234, 105090, 157326, 129914, 69840, 24672, 5248, 512

Offset

1,3

Links

Table of n, a(n) for n=1..55.

G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973), p. 25-27.

G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973). (Annotated scanned copy)

Formula

T(r, e) = A250484(r, e) - A250484(r-1, e).

Example

Triangle starts:
  1;
  1,   2;
  1,   6,   4;
  1,  14,  22,   8;
  1,  30,  86,  64,  16;
  1,  62, 294, 346, 168,  32;
  ...

Prog

(PARI) tabl(nn) = {v = vector(nn); v[1] = 1; for (n=2, nn, v[n] = 1 + t*v[n-1]^2/(1 - t*v[n-1]); ); pv = vector(nn, n, v[n]+O(t^(nn+1))); m = matrix(nn, nn, n, k, polcoeff(pv[n], k-1, t)); m = m ~; for (n= 2, nn, for (k=2, n, print1(m[n, k]-m[n, k-1], ", "); ); print(); ); }

Crossrefs

Cf. A000079 (right diagonal), A001003 (row sums), A250484.

Sequence in context: A114687 A137594 A112360 * A269505 A269479 A118040

Adjacent sequences: A250482 A250483 A250484 * A250486 A250487 A250488

Keyword

nonn,tabl

Author

Michel Marcus, Nov 24 2014

Status

approved