|
|
A210555
|
|
Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section.
|
|
2
|
|
|
1, 1, 2, 1, 3, 4, 1, 4, 7, 8, 1, 5, 10, 17, 16, 1, 6, 13, 28, 39, 32, 1, 7, 16, 41, 70, 89, 64, 1, 8, 19, 56, 109, 176, 199, 128, 1, 9, 22, 73, 156, 297, 426, 441, 256, 1, 10, 25, 92, 211, 456, 765, 1020, 967, 512, 1, 11, 28, 113, 274, 657, 1236, 1953, 2398
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
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)=2x*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
1...3...4
1...4...7....8
1...5...10...17...16
First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^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*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
|
|
|
|