login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210805 Triangle of coefficients of polynomials u(n,x) jointly generated with A210806; see the Formula section. 3
1, 1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 2, 6, 6, 5, 1, 3, 8, 14, 12, 8, 1, 3, 12, 22, 31, 23, 13, 1, 4, 15, 37, 56, 65, 43, 21, 1, 4, 20, 52, 102, 132, 132, 79, 34, 1, 5, 24, 76, 160, 260, 296, 261, 143, 55, 1, 5, 30, 100, 250, 446, 626, 639, 506, 256, 89, 1, 6, 35, 135, 360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
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
1...1
1...1...2
1...2...3...3
1...2...6...6...5
First three polynomials u(n,x): 1, 1 + x, 1 + x + 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 = 0; c = 0; 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[%] (* A210805 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210806 *)
CROSSREFS
Sequence in context: A328471 A227909 A301984 * A303842 A057041 A267177
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 17 10:33 EDT 2024. Contains 371763 sequences. (Running on oeis4.)