A167371 - OEIS

%I #11 Jan 26 2020 21:01:40

%S 1,0,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,

%T 1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,

%U 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1

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

%C Diagonal sums: A060576.

%C A167374*A154325 formatted as lower triangular matrix. - _Philippe Deléham_, Nov 19 2009

%F Sum_{k=0..n} T(n,k)*x^k = A000007(n), A046698(n+1), A111286(n+1), A027327(n) for x= 0, 1, 2, 3 respectively.

%F G.f.: (1+x^2*y)/(1-x*y). - _Philippe Deléham_, Nov 09 2013

%F T(n,k) = T(n-1,k-1) for n > 2, T(0,0) = T(1,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Nov 09 2013

%e Triangle begins:

%e   1;

%e   0, 1;

%e   0, 1, 1;

%e   0, 0, 1, 1;

%e   0, 0, 0, 1, 1;

%e   0, 0, 0, 0, 1, 1; ...

%Y Cf. A097806, A103451.

%K nonn,tabl

%O 0,1

%A _Philippe Deléham_, Nov 02 2009