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A226377
Lucas numbers differences triangle T(n,k), k<=n, where column k+1 holds the k-th differences of A000204, read by rows.
1
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, 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, 47, 199, 76, 29, 11, 4, 1, -1, -4, -1, -29, -76, -199
OFFSET
1,2
COMMENTS
Consecutive columns (i.e. k =1,2,3...) shift the Lucas sequence (A000204) down by 2 indices.
Diagonal (n=k) produces A061084, and Lucas numbers at increasingly negative indices for n=k>2.
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.
Compare A227431 which is a differences triangle for the Fibonacci sequence A000045.
FORMULA
T(n,1) = A000204(n) for n>0, T(n,k) = T(n,k-1) - T(n-1,k-1).
EXAMPLE
Triangle begins:
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;
47, 18, 7, 3, 2, 3, 7, 18;
76, 29, 11, 4, 1, -1, -4, -11, -29;
...
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Richard R. Forberg, Jul 31 2013
STATUS
approved