A250484 Square array: number of [0-r]-covering hierarchies with thickness <= e.

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 1, 0, 1, 1, 3, 7, 1, 0, 1, 1, 3, 11, 15, 1, 0, 1, 1, 3, 11, 37, 31, 1, 0, 1, 1, 3, 11, 45, 117, 63, 1, 0, 1, 1, 3, 11, 45, 181, 357, 127, 1, 0, 1, 1, 3, 11, 45, 197, 703, 1065, 255, 1, 0, 1, 1, 3, 11, 45, 197, 871, 2659, 3129, 511, 1, 0

Offset

0,13

Links

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

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

G.f. for column e: s(e) = 1 + t*s(e-1)^2/(1 - t*s(e-1)), with s(0) = 1.

Example

Table starts:
1 1   1    1    1    1    1    1 ...
0 1   1    1    1    1    1    1 ...
0 1   3    3    3    3    3    3 ...
0 1   7   11   11   11   11   11 ...
0 1  15   37   45   45   45   45 ...
0 1  31  117  181  197  197  197 ...
0 1  63  357  703  871  903  903 ...
0 1 127 1065 2659 3799 4215 4279 ...
...

Prog

(PARI) s(e) = if (e==0, 1, 1 + t*s(e-1)^2/(1 - t*s(e-1)));
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)); mattranspose(m); }

Crossrefs

Cf. A001003 (diagonal).

Sequence in context: A293960 A062719 A305161 * A294250 A117417 A231345

Adjacent sequences: A250481 A250482 A250483 * A250485 A250486 A250487

Keyword

nonn,tabl

Author

Michel Marcus, Nov 24 2014

Status

approved