|
| |
|
|
A210188
|
|
Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section.
|
|
3
|
|
|
|
1, 2, 2, 3, 7, 2, 4, 16, 11, 2, 5, 30, 36, 15, 2, 6, 50, 91, 64, 19, 2, 7, 77, 196, 204, 100, 23, 2, 8, 112, 378, 540, 385, 144, 27, 2, 9, 156, 672, 1254, 1210, 650, 196, 31, 2, 10, 210, 1122, 2640, 3289, 2366, 1015, 256, 35, 2, 11, 275, 1782, 5148, 8008
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Row sums: -1+(odd-indexed Fibonacci numbers): 1,4,12,...
Period of alternating row sums: (1,-,-2,-3,-2,0)
For a discussion and guide to related arrays, see A208510.
|
|
|
LINKS
|
Table of n, a(n) for n=1..60.
|
|
|
FORMULA
|
u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=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
3...7....2
4...16...11...2
5...30...36...15...2
First three polynomials v(n,x): 1, 2 + 2x , 3 + 7x + 2x^2.
|
|
|
MATHEMATICA
|
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, 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]
Flatten[%] (* A210187 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210188 *)
|
|
|
CROSSREFS
|
Cf. A210187, A208510.
Sequence in context: A260161 A195694 A021451 * A183442 A296019 A134232
Adjacent sequences: A210185 A210186 A210187 * A210189 A210190 A210191
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Clark Kimberling, Mar 18 2012
|
|
|
STATUS
|
approved
|
| |
|
|
