A226377 - OEIS

%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