A202451 Upper triangular Fibonacci matrix, by SW antidiagonals.

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

Offset: 1

Author

Clark Kimberling, Dec 19 2011

Keywords

• nonn
• tabl

Examples

			Northwest corner:
1...1...2...3...5...8...13...21...34
0...1...1...2...3...5....8...13...21
0...0...1...1...2...3....5....8...13
0...0...0...1...1...2....3....5....8
		

Links

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

Crossrefs

Cf. A000045, A188516, A202452, A202453, A202462.

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 matrix *)
TableForm[P]  (* A202452, lower triangular Fibonacci matrix *)
TableForm[F]  (* A202453, Fibonacci self-fusion matrix *)
TableForm[FactorInteger[F]]

Formula

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