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.

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

Offset

0,2

Comments

Riordan array ((1-x)/(1-3x), x^2/(1-3x)).

A skewed version of triangular array in A193723.

A202209*A007318 as infinite lower triangular matrices .

Links

Table of n, a(n) for n=0..54.

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

Cf. A000244, A025192, A081038, A183188 (antidiagonal sums)

Sequence in context: A321907 A361522 A137437 * A330609 A180047 A180397

Adjacent sequences: A183186 A183187 A183188 * A183190 A183191 A183192

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 14 2011

Status

approved