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

Author

Clark Kimberling, Dec 20 2011

Keywords

• nonn
• tabl

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.

Examples

			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
		

Links

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

Crossrefs

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

Programs

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 *)