

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



