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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208766 Triangle of coefficients of polynomials v(n,x) jointly generated with A208765; see the Formula section. 3
1, 1, 3, 1, 6, 7, 1, 9, 21, 19, 1, 12, 42, 76, 47, 1, 15, 70, 190, 235, 123, 1, 18, 105, 380, 705, 738, 311, 1, 21, 147, 665, 1645, 2583, 2177, 803, 1, 24, 196, 1064, 3290, 6888, 8708, 6424, 2047, 1, 27, 252, 1596, 5922, 15498, 26124, 28908, 18423 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

Subtriangle of the triangle given by (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 3, -2/3, -4/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 20 2012

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

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

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

From Philippe Deléham, Mar 20 2012: (Start)

As DELTA-triangle with 0<=k<=n :

G.f.: (1-x-y*x+3*y*x^2-4*y^2*x^2)/(1-2*x-y*x+x^2+y*x^2-4*y^2*x^2).

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1) + 4*T(n-2,k-2), T(0,0) = T(1,0) = T(2,0) = 1, T(1,1) = T(2,2) = 0, T(2,1) = 3 and T(n,k) = 0 if k<0 or if k>n. (End)

EXAMPLE

First five rows:

1

1...3

1...6....7

1...9....21...19

1...12...42...76...47

First five polynomials v(n,x):

1

1 + 3x

1 + 6x + 7x^2

1 + 9x + 21x^2 + 19x^3

1 + 12x + 42x^2 + 76x^3 + 47x^4

(1, 0, 0, 1, 0, 0, ...) DELTA (0, 3, -2/3, -4/3, 0, 0, ...) begins :

1

1, 0

1, 3, 0

1, 6, 7, 0

1, 9, 21, 19, 0

1, 12, 42, 76, 47, 0 . - Philippe Deléham, 20 2012

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] + (x + 1) 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[%]     (* A208765 *)

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

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

TableForm[cv]

Flatten[%]     (* A208766 *)

CROSSREFS

Cf. A208765, A208510.

Sequence in context: A198614 A239385 A124929 * A259454 A209696 A210749

Adjacent sequences:  A208763 A208764 A208765 * A208767 A208768 A208769

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 16 12:00 EDT 2019. Contains 328056 sequences. (Running on oeis4.)