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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208753 Triangle of coefficients of polynomials u(n,x) jointly generated with A208754; see the Formula section. 3
1, 1, 2, 1, 8, 1, 18, 4, 1, 32, 24, 1, 50, 80, 8, 1, 72, 200, 64, 1, 98, 420, 280, 16, 1, 128, 784, 896, 160, 1, 162, 1344, 2352, 864, 32, 1, 200, 2160, 5376, 3360, 384, 1, 242, 3300, 11088, 10560, 2464, 64, 1, 288, 4840, 21120, 28512, 11264, 896, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

u(n,x)=u(n-1,x)+2x*v(n-1,x),

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

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

EXAMPLE

First five rows:

1

1...2

1...8

1...18...4

1...32...24

First five polynomials u(n,x):

1

1 + 2x

1 + 8x

1 + 18x + 4x^2

1 + 32x + 24x^2

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];

v[n_, x_] := u[n - 1, 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[%]    (* A208753 *)

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

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

TableForm[cv]

Flatten[%]    (* A208754 *)

CROSSREFS

Cf. A208754, A208510.

Sequence in context: A009385 A008308 A176889 * A118931 A101280 A321280

Adjacent sequences:  A208750 A208751 A208752 * A208754 A208755 A208756

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 03 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 February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)