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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210792 Triangle of coefficients of polynomials v(n,x) jointly generated with A210791; see the Formula section. 3
1, 1, 2, 1, 5, 3, 1, 10, 11, 5, 1, 19, 28, 25, 8, 1, 36, 62, 81, 50, 13, 1, 69, 129, 218, 193, 98, 21, 1, 134, 261, 533, 597, 442, 185, 34, 1, 263, 522, 1235, 1631, 1559, 952, 343, 55, 1, 520, 1040, 2773, 4129, 4763, 3758, 1985, 625, 89, 1, 1033, 2071 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row n starts with 1 and ends with F(n+1), where F=A000045 (Fibonacci numbers).

Column 2: A052944

Row sums: A000244 (powers of 3)

Alternating row sums: A001333

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

Subtriangle of the triangle given by (1, 0, 1/2, 3/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 29 2012

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

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

Contribution from Philippe Deléham, Mar 29 2012. (Start)

As DELTA-triangle T(n,k) with 0<=k<=n :

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

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

EXAMPLE

First five rows:

1

1...2

1...5....3

1...10...11...5

1...19...28...25...8

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

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

1

1, 0

1, 2, 0

1, 5, 3, 0

1, 10, 11, 5, 0

1, 19, 28, 25, 8, 0

1, 36, 62, 81, 50, 13, 0

1, 69, 129, 218, 193, 98, 21, 0 . - Philippe Deléham, Mar 29 2012

MATHEMATICA

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

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

d[x_] := h + x; e[x_] := p + x;

v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;

j = 0; c = 0; h = -1; p = 2; f = 0;

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[%]    (* A210791 *)

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

TableForm[cv]

Flatten[%]    (* A210792 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]   (* A007051 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]   (* A000244 *)

Table[u[n, x] /. x -> -1, {n, 1, z}]  (* A001129 *)

Table[v[n, x] /. x -> -1, {n, 1, z}]  (* [A001333] *)

CROSSREFS

Cf. A210791, A208510.

Sequence in context: A240192 A264751 A209130 * A105728 A120095 A327631

Adjacent sequences:  A210789 A210790 A210791 * A210793 A210794 A210795

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 26 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 22 13:35 EDT 2019. Contains 328318 sequences. (Running on oeis4.)