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%I #9 Jul 31 2013 22:24:16
%S 1,3,2,4,1,-1,7,3,2,3,11,4,1,-1,-4,18,7,3,2,3,7,29,11,4,1,-1,-4,-11,
%T 47,18,7,3,2,3,7,18,76,29,11,4,1,-1,-4,-11,-29,123,47,18,7,3,2,3,7,18,
%U 47,199,76,29,11,4,1,-1,-4,-1,-29,-76,-199
%N Lucas numbers differences triangle T(n,k), k<=n, where column k+1 holds the k-th differences of A000204, read by rows.
%C Consecutive columns (i.e. k =1,2,3...) shift the Lucas sequence (A000204) down by 2 indices.
%C Diagonal (n=k) produces A061084, and Lucas numbers at increasingly negative indices for n=k>2.
%C Row sums equal A203976(n) for n=>1, which equals Lucas numbers A000204(n) if n is odd, and 5 * A000045(2*n) (Fibonacci) if n is even.
%C Compare A227431 which is a differences triangle for the Fibonacci sequence A000045.
%F T(n,1) = A000204(n) for n>0, T(n,k) = T(n,k-1) - T(n-1,k-1).
%e Triangle begins:
%e 1;
%e 3, 2;
%e 4, 1, -1;
%e 7, 3, 2, 3;
%e 11, 4, 1, -1, -4;
%e 18, 7, 3, 2, 3, 7;
%e 29, 11, 4, 1, -1, -4, -11;
%e 47, 18, 7, 3, 2, 3, 7, 18;
%e 76, 29, 11, 4, 1, -1, -4, -11, -29;
%e ...
%Y Cf. A000204, A203976
%K sign,tabl
%O 1,2
%A _Richard R. Forberg_, Jul 31 2013
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