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A154312 Triangle T(n,k), 0<=k<=n, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,0,0,...] DELTA [2,-1/2,-1/2,2,0,0,0,0,0,0,0 ...] where DELTA is the operator defined in A084938 .

%I A154312 #10 Nov 02 2013 05:30:46
%S A154312 1,0,2,0,1,3,0,0,3,5,0,0,0,7,9,0,0,0,0,15,17,0,0,0,0,0,31,33,0,0,0,0,
%T A154312 0,0,63,65,0,0,0,0,0,0,0,127,129,0,0,0,0,0,0,0,0,255,257,0,0,0,0,0,0,
%U A154312 0,0,0,511,513,0,0,0,0,0,0,0,0,0,0,1023,1025,0,0,0,0,0,0,0,0,0,0,0,2047
%N A154312 Triangle T(n,k), 0<=k<=n, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,0,0,...] DELTA [2,-1/2,-1/2,2,0,0,0,0,0,0,0 ...] where DELTA is the operator defined in A084938 .
%C A154312 Column sums give A003945.
%F A154312 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)= A040000(n), A094373(n), A000079(n), A083329(n), A095121(n), A154117(n), A131128(n), A154118(n), A131130(n), A154251(n), A154252(n) for x = -1,0,1,2,3,4,5,6,7,8,9 respectively.
%F A154312 G.f.: (1-x*y+x^2*y-x^2*y^2)/(1-3*x*y+2*x^2*y^2). - _Philippe Deléham_, Nov 02 2013
%F A154312 T(n,k) = 3*T(n-1,k-1) - 2*T(n-2,k-2), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(2,0) = 0, T(2,1) = 1, T(2,2) = 3, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Nov 02 2013
%e A154312 Triangle begins:
%e A154312 1;
%e A154312 0, 2;
%e A154312 0, 1, 3;
%e A154312 0, 0, 3, 5;
%e A154312 0, 0, 0, 7, 9;
%e A154312 0, 0, 0, 0, 15, 17; ...
%Y A154312 Cf. A000225, A094373
%K A154312 nonn,tabl
%O A154312 0,3
%A A154312 _Philippe Deléham_, Jan 07 2009