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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209772 Triangle of coefficients of polynomials v(n,x) jointly generated with A209771; see the Formula section. 3
1, 2, 2, 2, 5, 4, 3, 9, 14, 8, 3, 14, 32, 36, 16, 4, 20, 60, 100, 88, 32, 4, 27, 100, 220, 288, 208, 64, 5, 35, 154, 420, 728, 784, 480, 128, 5, 44, 224, 728, 1568, 2240, 2048, 1088, 256, 6, 54, 312, 1176, 3024, 5376, 6528, 5184, 2432, 512, 6, 65, 420 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums:  1,0,1,0,1,0,1,0,...

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),

v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2...2

2...5....4

3...9....14...8

3...14...32...36...16

First three polynomials v(n,x): 1, 2 + 2x , 2 + 5x + 4x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];

v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A209771 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A209772 *)

CROSSREFS

Cf. A209671, A208510.

Sequence in context: A208512 A208908 A209558 * A147293 A134634 A103286

Adjacent sequences:  A209769 A209770 A209771 * A209773 A209774 A209775

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 2012

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 October 16 05:41 EDT 2019. Contains 328044 sequences. (Running on oeis4.)