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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208917 Triangle of coefficients of polynomials u(n,x) jointly generated with A208918; see the Formula section. 3
1, 1, 2, 1, 4, 8, 1, 6, 16, 24, 1, 8, 24, 56, 80, 1, 10, 32, 96, 208, 256, 1, 12, 40, 144, 384, 736, 832, 1, 14, 48, 200, 608, 1472, 2624, 2688, 1, 16, 56, 264, 880, 2496, 5632, 9216, 8704, 1, 18, 64, 336, 1200, 3840, 10112, 21120, 32256, 28160, 1, 20, 72 (list; table; 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..58.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

1...4...8

1...6...16...24

1...8...24...56...80

First five polynomials u(n,x):

1

1 + 2x

1 + 4x + 8x^2

1 + 6x + 16x^2 + 24x^3

1 + 8x + 24x^2 + 56x^3 + 80x^4

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_] := 2 x*u[n - 1, x] + 2 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[%]    (* A208917 *)

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

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

TableForm[cv]

Flatten[%]    (* A208918 *)

CROSSREFS

Cf. A208918, A208510.

Sequence in context: A001933 A038557 A011234 * A161381 A220579 A128412

Adjacent sequences:  A208914 A208915 A208916 * A208918 A208919 A208920

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 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 23:30 EDT 2019. Contains 328103 sequences. (Running on oeis4.)