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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208758 Triangle of coefficients of polynomials v(n,x) jointly generated with A208757; see the Formula section. 3
1, 0, 3, 0, 1, 8, 0, 1, 4, 22, 0, 1, 4, 16, 60, 0, 1, 4, 18, 56, 164, 0, 1, 4, 20, 68, 188, 448, 0, 1, 4, 22, 80, 248, 608, 1224, 0, 1, 4, 24, 92, 312, 864, 1920, 3344, 0, 1, 4, 26, 104, 380, 1152, 2928, 5952, 9136, 0, 1, 4, 28, 116, 452, 1472, 4128, 9696, 18192 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

As triangle T(n,k) with 0<=k<=n, it is (0, 1/3, 2/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (3, -1/3, -2/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 02 2012

LINKS

Table of n, a(n) for n=1..65.

FORMULA

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

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

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

As triangle T(n,k), 0<=k<=n : G.f.: (1-x-y*x)/(1-(1+2*y)*x -2*y(y-1)*x^2). - Philippe Deléham, Mar 02 2012

As triangle T(n,k), 0<=k<=n : T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) + 2*T(n-2,k-2) with T(0,0) = 1, T(1,0) = 0, T(1,1) = 3 and T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 02 2012

EXAMPLE

First five rows:

1

0...3

0...1...8

0...1...4...22

0...1...4...16...60

First five polynomials v(n,x):

1

3x

x + 8x^2

x + 4x^2 + 22x^3

x + 4x^2 + 16x^3 + 60^x4

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

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[%]  (* A208757 *)

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

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

TableForm[cv]

Flatten[%]  (* A208758 *)

CROSSREFS

Cf. A208757, A208510.

Sequence in context: A216806 A290776 A172249 * A320161 A291763 A161129

Adjacent sequences:  A208755 A208756 A208757 * A208759 A208760 A208761

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 02 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 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)