A202502 Modified lower triangular Fibonacci matrix, by antidiagonals.

1, 0, 2, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 3, 8, 0, 0, 0, 2, 5, 13, 0, 0, 0, 1, 3, 8, 21, 0, 0, 0, 0, 2, 5, 13, 34, 0, 0, 0, 0, 1, 3, 8, 21, 55, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55, 144, 0, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 233, 0, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55

Offset

1,3

Comments

This matrix, P, is used to form the Fibonacci self-fission matrix as the product P*Q, where Q is the upper triangular Fibonacci matrix, A202451. To form P, delete the main diagonal of the transpose of Q.

Links

Table of n, a(n) for n=1..89.

Clark Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195-202.

Example

Northwest corner:
1...0...0...0...0...0...0...0...0
2...1...0...0...0...0...0...0...0
3...2...1...0...0...0...0...0...0
5...3...2...1...1...0...0...0...0
8...5...3...2...1...1...0...0...0

Mathematica

n = 14;
Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];
Qt = Transpose[Q]; P1 = Qt - IdentityMatrix[n];
P = P1[[Range[2, n], Range[1, n]]];
F = P.Q;
Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202502 as a sequence *)
Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202451 as a sequence *)
Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202503 as a sequence *)
TableForm[P]  (* A202502, modified lower triangular Fibonacci matrix *)
TableForm[Q] (* A202451, upper tri. Fibonacci matrix *)
TableForm[F] (* A202503, Fibonacci self-fission matrix *)

Crossrefs

Cf. A202503, A202451, A202452, A202453, A000045.

Sequence in context: A338849 A338838 A132213 * A219839 A154312 A236076

Adjacent sequences: A202499 A202500 A202501 * A202503 A202504 A202505

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 20 2011

Status

approved