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A193559 Augmentation of the triangular array |A123191|.  See Comments. 1
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 (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..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

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Last modified March 19 13:08 EDT 2019. Contains 321330 sequences. (Running on oeis4.)