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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209769 Triangle of coefficients of polynomials u(n,x) jointly generated with A209770; see the Formula section. 3
1, 1, 2, 3, 5, 3, 5, 12, 11, 5, 9, 26, 34, 24, 8, 15, 53, 88, 86, 48, 13, 25, 104, 210, 258, 200, 93, 21, 41, 198, 470, 695, 680, 440, 175, 34, 67, 369, 1007, 1737, 2043, 1671, 929, 323, 55, 109, 676, 2085, 4107, 5625, 5529, 3895, 1901, 587, 89, 177 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 1: A001595

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

Row sums: 1,3,11,33,101,303,911,2733,... A081250

Alternating row sums: 1,-1,1,-1,1,-1,... A033999

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

3...5....3

5...12...11...5

9...26...34...24...8

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

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A209769 *)

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

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

TableForm[cv]

Flatten[%]    (* A209770 *)

CROSSREFS

Cf. A209770, A208510.

Sequence in context: A224887 A151571 A193957 * A114230 A209753 A185191

Adjacent sequences:  A209766 A209767 A209768 * A209770 A209771 A209772

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 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 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)