|
|
A209999
|
|
Triangle of coefficients of polynomials u(n,x) jointly generated with A210287; see the Formula section.
|
|
4
|
|
|
1, 2, 2, 4, 6, 3, 7, 16, 13, 4, 12, 36, 44, 24, 5, 20, 76, 122, 100, 40, 6, 33, 152, 306, 332, 201, 62, 7, 54, 294, 712, 968, 783, 370, 91, 8, 88, 554, 1573, 2572, 2614, 1666, 637, 128, 9, 143, 1024, 3339, 6392, 7829, 6296, 3277, 1040, 174, 10, 232, 1864
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Column 1: -1+F(n+2), where F=000045 (Fibonacci numbers)
Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...
For a discussion and guide to related arrays, see A208510.
|
|
LINKS
|
|
|
FORMULA
|
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
v(n,x)=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
2....2
4....6....3
7....16...13...4
12...36...44...24...5
First three polynomials u(n,x): 1, 2 + 2x, 4 + 6x + 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] + 1;
v[n_, x_] := u[n - 1, x] + (x + 1)*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]
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|