A193597 Augmentation of the triangle A193596. See Comments.

1, 1, 1, 1, 2, 2, 1, 4, 6, 5, 1, 6, 17, 21, 16, 1, 9, 34, 78, 86, 61, 1, 12, 69, 201, 397, 401, 269, 1, 16, 116, 522, 1282, 2250, 2113, 1350, 1, 20, 194, 1074, 4099, 8900, 14187, 12509, 7650, 1, 25, 292, 2172, 10078, 34044, 67316, 99102, 82713, 48634, 1

Offset

0,5

Comments

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

Links

Table of n, a(n) for n=0..55.

Example

First 5 rows of A193596:
1
1...1
1...1...1
1...2...2...1
1...2...3...2...1

Mathematica

p[n_, k_] := Ceiling[Binomial[n, k]/2]
Table[p[n, k], {n, 0, 10}, {k, 0, n}]
Flatten[%]  (* A193596 *)
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 10}]] (* A193597 *)
Flatten[Table[v[n], {n, 0, 10}]]

Crossrefs

Cf. A193596, A193091.

Sequence in context: A111062 A369632 A363493 * A191490 A061598 A328873

Adjacent sequences: A193594 A193595 A193596 * A193598 A193599 A193600

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 31 2011

Status

approved