A202452 Lower triangular Fibonacci matrix, by SW antidiagonals.

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

Offset: 1

Author

Clark Kimberling, Dec 19 2011

Keywords

• nonn
• tabl

Examples

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

Links

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

Crossrefs

Cf. A202451, A202453, A202462, A188516, A000045.

Programs

Mathematica

n = 12;
Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];
P = Transpose[Q]; F = P.Q;
Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202451 as a sequence *)
Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202452 as a sequence *)
Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202453 as a sequence *)
TableForm[Q]  (* A202451, upper triangular Fibonacci array *)
TableForm[P]  (* A202452, lower triangular Fibonacci array *)
TableForm[F]  (* A202453, Fibonacci self-fusion matrix *)
TableForm[FactorInteger[F]]

Formula

Column n consists of n-1 zeros followed by the Fibonacci sequence (1,1,2,3,5,8,...).