login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193604 Augmentation of the triangle A055248.  See Comments. 1
1, 2, 1, 8, 8, 3, 64, 88, 62, 19, 1024, 1664, 1568, 896, 233, 32768, 58368, 64128, 49248, 23890, 5385, 2097152, 3932160, 4703232, 4249728, 2800488, 1179656, 233787, 268435456, 517996544, 649887744, 645547008, 507802304, 293645688, 108978862 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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..34.

EXAMPLE

First five rows of A193604:

1

2.....1

8.....8.....3

64....88....62....19

1024..1664..1568..896...233

MATHEMATICA

u[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] (* A055248 *)

p[n_, k_] := u[n, n - k]

Table[p[n, k], {n, 0, 5}, {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}]] (* A193604 *)

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

CROSSREFS

Cf. A055248, A193091.

Sequence in context: A321369 A286724 A123516 * A016446 A254794 A086657

Adjacent sequences:  A193601 A193602 A193603 * A193605 A193606 A193607

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 February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)