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!)
A193859 Mirror of the triangle A193858. 3
1, 3, 2, 7, 10, 4, 15, 34, 28, 8, 31, 98, 124, 72, 16, 63, 258, 444, 392, 176, 32, 127, 642, 1404, 1672, 1136, 416, 64, 255, 1538, 4092, 6152, 5616, 3104, 960, 128, 511, 3586, 11260, 20488, 23536, 17440, 8128, 2176, 256, 1023, 8194, 29692, 63496 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A193859 is obtained by reversing the rows of the triangle A193858.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

Write w(n,k) for the triangle at A193858.  The triangle at A193859 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

3....2

7....10...4

15...34...28...8

31...98...124..72...16

63...258..444..392..176..32

MATHEMATICA

z = 10;

p[n_, x_] := (x + 1)^n;

q[n_, x_] := (2 x + 1)^n;

p1[n_, k_] := Coefficient[p[n, x], x^k];

p1[n_, 0] := p[n, x] /. x -> 0;

d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

h[n_] := CoefficientList[d[n, x], {x}]

TableForm[Table[Reverse[h[n]], {n, 0, z}]]

Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193858 *)

TableForm[Table[h[n], {n, 0, z}]]

Flatten[Table[h[n], {n, -1, z}]]   (* A193859 *)

CROSSREFS

Cf. A193858.

Sequence in context: A118966 A018891 A034423 * A174330 A099329 A182871

Adjacent sequences:  A193856 A193857 A193858 * A193860 A193861 A193862

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 07 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 September 22 12:00 EDT 2021. Contains 347607 sequences. (Running on oeis4.)