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Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
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%I #8 Sep 08 2013 19:59:25

%S 1,1,1,2,3,1,0,4,5,1,0,0,6,7,1,0,0,0,8,9,1,0,0,0,0,10,11,1,0,0,0,0,0,

%T 12,13,1,0,0,0,0,0,0,14,15,1,0,0,0,0,0,0,0,16,17,1,0,0,0,0,0,0,0,0,18,

%U 19,1,0,0,0,0,0,0,0,0,0,20,21,1,0,0,0,0,0,0,0,0,0,0,22,23,1,0,0,0,0,0,0,0,0

%N Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

%C Row sums = A111284(n+1), Diagonal sums = A109613(n).

%F T(n,k) = 2*T(n-1,k-1) - T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(3,0) = 0, T(3,1) = 4. - _Philippe Deléham_, Feb 18 2012

%F G.f.: (1+(1-y)*x+(2+y)*x^2)/(1-y*x)^2. - _Philippe Deléham_, Feb 18 2012

%F Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A130779(n), A111284(n+1), A167667(n), A167682(n) for x = -1, 0, 1, 2, 3 respectively. - _Philippe Deléham_, Feb 18 2012

%e Triangle begins :

%e 1 ;

%e 1, 1 ;

%e 2, 3, 1 ;

%e 0, 4, 5, 1 ;

%e 0, 0, 6, 7, 1 ;

%e 0, 0, 0, 8, 9, 1 ;

%e 0, 0, 0, 0, 10, 11, 1 ; ...

%Y Cf. A000012, A005408, A005843

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Nov 08 2009