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!)
A210563 Triangle of coefficients of polynomials u(n,x) jointly generated with A210564; see the Formula section. 3
1, 1, 2, 1, 3, 5, 1, 3, 10, 13, 1, 3, 11, 32, 34, 1, 3, 11, 40, 99, 89, 1, 3, 11, 41, 141, 299, 233, 1, 3, 11, 41, 152, 482, 887, 610, 1, 3, 11, 41, 153, 556, 1604, 2595, 1597, 1, 3, 11, 41, 153, 570, 1998, 5217, 7508, 4181, 1, 3, 11, 41, 153, 571, 2113, 7042 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Last terms in rows: odd-indexed Fibonacci numbers
Limiting row: A001835
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...3...5
1...3...10...13
1...3...11...32...34
First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 5x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A210563 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210564 *)
CROSSREFS
Sequence in context: A089984 A284429 A062105 * A236311 A347773 A368563
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 23 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 March 29 22:15 EDT 2024. Contains 371282 sequences. (Running on oeis4.)