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A227431

Fibonacci differences triangle, T(n,k), k<=n, where column k holds the k-th difference of A000045, read by rows.

1, 1, 0, 2, 1, 1, 3, 1, 0, -1, 5, 2, 1, 1, 2, 8, 3, 1, 0, -1, -3, 13, 5, 2, 1, 1, 2, 5, 21, 8, 3, 1, 0, -1, -3, -8, 34, 13, 5, 2, 1, 1, 2, 5, 13, 55, 21, 8, 3, 1, 0, -1, -3, -8, -21, 89, 34, 13, 5, 2, 1, 1, 2, 5, 13, 34, 144, 55, 21, 8, 3, 1, 0, -1, -3, -8, -21

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OFFSET

1,4

COMMENTS

Consecutive columns (i.e., k = 1, 2, 3, ...) shift the Fibonacci sequence down by 2 indices.

Diagonal (n = k) produces Fibonacci numbers at increasingly negative indices for n = k > 2. See A039834.

Row sums equal A005013(n), which equals Fibonacci A000045(n), if n is even, and equals Lucas numbers A000204(n) if n is odd.

(Rows that sum to Lucas numbers have all positive values.)

LINKS

T. D. Noe, Rows n = 1..100 of triangle, flattened

FORMULA

T(n,1) = F(n) for n > 0, where F(n) = A000045(n), T(n,k) = T(n,k-1) - T(n-1,k-1).