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A357724

Triangular array read by rows: T(n,k) = Fib(n) mod Fib(k) for 1 <= k <= n, where Fib(k) = A000045(k).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 3, 0, 0, 0, 1, 1, 3, 5, 0, 0, 0, 1, 0, 1, 5, 8, 0, 0, 0, 0, 1, 4, 2, 8, 13, 0, 0, 0, 1, 1, 0, 7, 3, 13, 21, 0, 0, 0, 1, 2, 4, 1, 11, 5, 21, 34, 0, 0, 0, 0, 0, 4, 0, 1, 18, 8, 34, 55, 0, 0, 0, 1, 2, 3, 1, 12, 2, 29, 13, 55, 89, 0, 0, 0, 1, 2

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OFFSET

1,14

COMMENTS

For k > 2, T(n,k) = 0 if and only if n is divisible by k. Otherwise, let n = q*k+r with 0 < r < k and k > 2.

If q is even and k is even, or q == 0 (mod 4) and k is odd, T(n,k) = A000045(r).

If q == 2 (mod 4) and k is odd, T(n,k) = A000045(k) - A000045(r).

If q == 1 (mod 4) and r is odd, or q == 3 (mod 4) and r+k is odd, T(n,k) = A000045(k-r).

If q == 1 (mod 4) and r is even, or q == 3 (mod 4) and r+k is even, T(n,k) = A000045(k) - A000045(k-r).

LINKS

Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

EXAMPLE