login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193602 Augmentation of the triangle A122366.  See Comments. 1
1, 1, 3, 1, 8, 19, 1, 15, 80, 172, 1, 24, 221, 971, 1967, 1, 35, 492, 3547, 13809, 26832, 1, 48, 955, 10186, 62840, 224529, 422609, 1, 63, 1684, 24890, 222132, 1226003, 4102449, 7525966, 1, 80, 2765, 54077, 658319, 5167948, 26193697, 83159133 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..43.

EXAMPLE

First five rows of A193602:

1

1...3

1...8....19

1...15...80...172

1...24...221..971...1967

MATHEMATICA

p[n_, k_] := Binomial[2 n + 1, k] (* A122366 *)

Table[p[n, k], {n, 0, 7}, {k, 0, n}]

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}]] (* A193602 *)

Flatten[Table[v[n], {n, 0, 8}]]

CROSSREFS

Cf. A122366, A193091.

Sequence in context: A221736 A077108 A075847 * A221125 A049967 A221780

Adjacent sequences:  A193599 A193600 A193601 * A193603 A193604 A193605

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 31 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 6 11:14 EDT 2020. Contains 334827 sequences. (Running on oeis4.)