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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208760 Triangle of coefficients of polynomials v(n,x) jointly generated with A208759; see the Formula section. 3
1, 1, 3, 1, 5, 8, 1, 7, 20, 22, 1, 9, 36, 72, 60, 1, 11, 56, 158, 244, 164, 1, 13, 80, 288, 632, 796, 448, 1, 15, 108, 470, 1320, 2376, 2528, 1224, 1, 17, 140, 712, 2420, 5592, 8544, 7872, 3344, 1, 19, 176, 1022, 4060, 11372, 22368, 29712, 24144, 9136 (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, -1/3, 1/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 3, -1/3, -2/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 18 2012

LINKS

Table of n, a(n) for n=1..55.

FORMULA

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

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

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

Contribution from Philippe Deléham, Mar 18 2012. (Start)

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

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

T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + 2*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 oe if k>n. (End)

EXAMPLE

First five rows:

1

1...3

1...5...8

1...7...20...22

1...9...36...72...60

First five polynomials v(n,x):

1

1 + 3x

1 + 5x + 8x^2

1 + 7x + 20x^2 + 22x^3

1 + 9x + 36x^2 + 72x^3 + 60x^4

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

1

1, 0

1, 3, 0

1, 5, 8, 0

1, 7, 20, 22, 0

1, 9, 36, 72, 60, 0

1, 11, 56, 158, 244, 164, 0 . Philippe Deléham, Mar 18 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_] := (x + 1)*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[%]  (* A208759 *)

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

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

TableForm[cv]

Flatten[%]  (* A208760 *)

CROSSREFS

Cf. A208759, A208510.

Sequence in context: A261712 A038738 A210741 * A116647 A063858 A209831

Adjacent sequences:  A208757 A208758 A208759 * A208761 A208762 A208763

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 20 15:15 EDT 2019. Contains 328267 sequences. (Running on oeis4.)