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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210801 Triangle of coefficients of polynomials u(n,x) jointly generated with A210802; see the Formula section. 3
1, 3, 1, 6, 5, 2, 12, 15, 10, 3, 21, 39, 37, 19, 5, 39, 90, 111, 81, 35, 8, 66, 198, 300, 281, 171, 64, 13, 120, 414, 750, 855, 659, 346, 115, 21, 201, 846, 1776, 2391, 2230, 1474, 684, 205, 34, 363, 1683, 4044, 6255, 6828, 5441, 3170, 1323, 362, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n ends with F(n), where F=A000045 (Fibonacci numbers).

Row sums:  A003462

Alternating row sums:  1,2,3,4,5,6,7,8,...

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

LINKS

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

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3....1

6....5....2

12...15...10...3

21...39...37...19...5

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

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 = 1; c = 1; h = 2; p = -1; f = 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[%]   (* A210801 *)

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

TableForm[cv]

Flatten[%]   (* A210802 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A003462 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A003462 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A000027 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A077898 *)

CROSSREFS

Cf. A210802, A208510.

Sequence in context: A322427 A209149 A210602 * A153091 A210593 A179069

Adjacent sequences:  A210798 A210799 A210800 * A210802 A210803 A210804

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 27 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 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)