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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
OFFSET
0,5
COMMENTS
For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
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
Sequence in context: A111062 A369632 A363493 * A191490 A061598 A328873
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jul 31 2011
STATUS
approved