A183189 - OEIS

%I #13 Oct 16 2024 06:02:43

%S 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,

%T 1458,1053,216,11,0,0,0,0,4374,3645,945,78,1,0,0,0,0,13122,12393,3888,

%U 450,14,0,0,0,0,0

%N 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.

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

%C A skewed version of triangular array in A193723.

%C A202209*A007318 as infinite lower triangular matrices.

%F G.f.: (1-x)/(1-3*x-y*x^2).

%F T(n,k) = Sum_{j, j>=0} T(n-2-j,k-1)*3^j.

%F T(n,k) = 3*T(n-1,k) + T(n-2,k-1).

%F 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.

%e Triangle begins:

%e   1

%e   2, 0

%e   6, 1, 0

%e   18, 5, 0, 0

%e   54, 21, 1, 0, 0

%e   162, 81, 8, 0, 0, 0

%e   486, 297, 45, 1, 0, 0, 0

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

%K nonn,tabl

%O 0,2

%A _Philippe Deléham_, Dec 14 2011