A193559 Augmentation of the triangular array |A123191|. See Comments.

1, 1, 1, 1, 4, 2, 1, 7, 17, 7, 1, 10, 41, 82, 32, 1, 13, 74, 238, 434, 166, 1, 16, 116, 502, 1412, 2446, 926, 1, 19, 167, 901, 3317, 8587, 14405, 5419, 1, 22, 227, 1462, 6581, 21802, 53381, 87610, 32816, 1, 25, 296, 2212, 11717, 46681, 143666, 338038

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..52.

Example

First five rows of |A123191|:
1
1...1
1...3...1
1...3...3...1
1...3...3...3...1
First 5 rows of A193559:
1
1...1
1...4...2
1...7...17...7
1...10..41...82...32

Mathematica

p[n_, k_] := If[Or[k == 0, k == n], 1, 3]
Table[p[n, k], {n, 0, 5}, {k, 0, n}]  (* Abs. value of A123191 *)
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, 6}]] (* A193559 *)
Flatten[Table[v[n], {n, 0, 10}]]

Crossrefs

Cf. A193091.

Sequence in context: A142147 A291977 A142073 * A135294 A175938 A117016

Adjacent sequences: A193556 A193557 A193558 * A193560 A193561 A193562

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 30 2011

Status

approved