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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209149 Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section. 5
1, 3, 1, 6, 5, 1, 12, 16, 7, 1, 24, 44, 30, 9, 1, 48, 112, 104, 48, 11, 1, 96, 272, 320, 200, 70, 13, 1, 192, 640, 912, 720, 340, 96, 15, 1, 384, 1472, 2464, 2352, 1400, 532, 126, 17, 1, 768, 3328, 6400, 7168, 5152, 2464, 784, 160, 19, 1, 1536, 7424 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,2,2,2,2,2,2,2,2,2,2,2,2,...

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

As triangle T(n,k) with 0<=k<=n, it is (3, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 08 2012

A skew triangle of A209144. - Philippe Deléham, Mar 08 2012

Riordan array ( (1 + x)/(1 - 2*x), x/(1 - 2*x) ). Cf. A118800. Matrix inverse is a signed version of A112626. - Peter Bala, Jul 17 2013

LINKS

Table of n, a(n) for n=1..57.

FORMULA

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

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

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

As DELTA-triangle :

T(n,k) = 2*T(n-1,k) + T(n-1,k-1), T(0,0) = 1, T(1,0) = 3, T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 08 2012

As DELTA-triangle : G.f. is (1+x)/(1-2*x-yx). - Philippe Deléham, Mar 08 2012

EXAMPLE

First five rows:

1

3....1

6....5....1

12...16...7....1

24...44...30...9...1

First three polynomials v(n,x): 1, 3 + x, 6 + 5x + x^2.

v(1,x) = 1

v(2,x) = 3 + x

v(3,x) = (3 + x)*(2 + x)

v(4,x) = (3 + x)*(2 + x)^2

v(5,x) = (3 + x)*(2 + x)^3

v(n,x) = (3 + x)*(2 + x)^(n-2)for n>1 . - Philippe Deléham, Mar 08 2012

MATHEMATICA

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

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

v[n_, x_] := u[n - 1, x] + (x + 1)*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[%]    (* A209148 *)

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

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

TableForm[cv]

Flatten[%]    (* A209149 *)

CROSSREFS

Cf. A209144, A209148, A208510.

Sequence in context: A153641 A133545 A210214 * A210602 A210801 A153091

Adjacent sequences:  A209146 A209147 A209148 * A209150 A209151 A209152

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 19 17:22 EDT 2018. Contains 305594 sequences. (Running on oeis4.)