|
| |
|
|
A208511
|
|
Triangle of coefficients of polynomials u(n,x) jointly generated with A208512; see the Formula section.
|
|
3
|
|
|
|
1, 1, 1, 1, 3, 2, 1, 5, 7, 4, 1, 7, 14, 16, 8, 1, 9, 23, 37, 36, 16, 1, 11, 34, 69, 94, 80, 32, 1, 13, 47, 114, 195, 232, 176, 64, 1, 15, 62, 174, 354, 528, 560, 384, 128, 1, 17, 79, 251, 588, 1041, 1384, 1328, 832, 256, 1, 19, 98, 347, 916, 1863, 2938, 3536
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
LINKS
|
|
|
|
FORMULA
|
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=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...1
1...3...2
1...5...7....4
1...7...14...16...8
First five polynomials u(n,x):
1
1 + x
1 + 3x + 2x^2
1 + 5x + 7x^2 + 4x^3
1 + 7x + 14x^2 + 16x^3 + 8x^4
|
|
|
MATHEMATICA
|
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 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]
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
|
| |
|
|
