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!)
A210231 Triangle of coefficients of polynomials u(n,x) jointly generated with A210232; see the Formula section. 3
1, 2, 1, 3, 4, 1, 4, 8, 7, 1, 5, 14, 18, 11, 1, 6, 21, 39, 36, 16, 1, 7, 30, 69, 93, 66, 22, 1, 8, 40, 114, 192, 199, 113, 29, 1, 9, 52, 172, 360, 474, 393, 183, 37, 1, 10, 65, 250, 610, 997, 1068, 729, 283, 46, 1, 11, 80, 345, 980, 1882, 2501, 2238, 1285, 421 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...1
3...4....1
4...8....7....1
5...14...18...11...1
First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A210231 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210232 *)
CROSSREFS
Sequence in context: A072506 A188236 A181851 * A180378 A208341 A201634
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 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 16 04:17 EDT 2024. Contains 371696 sequences. (Running on oeis4.)