login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 03:48 EST 2022. Contains 358672 sequences. (Running on oeis4.)