|
|
A183189
|
|
Triangle T(n,k), read by rows, given by (2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
|
|
0
|
|
|
1, 2, 0, 6, 1, 0, 18, 5, 0, 0, 54, 21, 1, 0, 0, 162, 81, 8, 0, 0, 0, 486, 297, 45, 1, 0, 0, 0, 1458, 1053, 216, 11, 0, 0, 0, 0, 4374, 3645, 945, 78, 1, 0, 0, 0, 0, 13122, 12393, 3888, 450, 14, 0, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Riordan array ((1-x)/(1-3x), x^2/(1-3x)).
A skewed version of triangular array in A193723.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: ((1-x)/(1-3x-y*x^2).
T(n,k) = Sum_{j, j>=0} T(n-2-j,k-1)*3^j.
T(n,k) = 3*T(n-1,k) + T(n-2,k-1).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A057682(n+1), A000079(n), A122367(n), A025192(n), A052924(n), A104934(n), A202206(n), A122117(n), A197189(n) for x = -3, -2, -1, 0, 1, 2, 3, 4, 5 respectively.
|
|
EXAMPLE
|
Triangle begins :
1
2, 0
6, 1, 0
18, 5, 0, 0
54, 21, 1, 0, 0
162, 81, 8, 0, 0, 0
486, 297, 45, 1, 0, 0, 0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|