A112906 - OEIS

%I #3 Mar 30 2012 18:59:12

%S 1,0,3,0,1,10,0,0,6,33,0,0,1,29,109,0,0,0,9,126,360,0,0,0,1,57,516,

%T 1189,0,0,0,0,12,306,2034,3927,0,0,0,0,1,94,1491,7807,12970,0,0,0,0,0,

%U 15,600,6813,29382,42837,0,0,0,0,0,1,140,3385,29737,108923,141481,0,0,0,0,0,0

%N A skew generalized Pascal triangle.

%C Main diagonal is A006190. Row sums are A007482. Column sums are A001076(n+1). Compare with [0,1/3,-1/3,0,0,..] DELTA [3,1/3,-1/3,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-3x-x^2),x/(1-3x-x^2)).

%F G.f.: 1/(1-3xy(1+x/3)-x^2*y^2); T(n, k)=sum{j=0..floor((2k-n)/2), C(k-j, n-k)C(2k-n, j)3^(2k-2j-n)}; T(n, k) = 3*T(n-1, k-1)+T(n-2, k-1)+T(n-2, k-2).

%e Triangle begins

%e 1;

%e 0, 3;

%e 0, 1, 10;

%e 0, 0, 6, 33;

%e 0, 0, 1, 29, 109;

%e 0, 0, 0, 9, 126, 360,

%e 0, 0, 0, 1, 57, 516, 1189;

%e 0, 0, 0, 0, 12, 306, 2034, 3927;

%e 0, 0, 0, 0, 1, 94, 1491, 7809, 12970;

%Y Cf. A112899.

%K easy,nonn,tabl

%O 0,3

%A _Paul Barry_, Oct 05 2005