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A193597 Augmentation of the triangle A193596.  See Comments. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A112307 A228336 A111062 * A191490 A061598 A071946

Adjacent sequences:  A193594 A193595 A193596 * A193598 A193599 A193600

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 2011

STATUS

approved

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Last modified June 4 17:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)