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

1,4

Links

Table of n, a(n) for n=1..78.

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

Formula

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

Example

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

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]]

Crossrefs

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

Sequence in context: A063173 A120111 A130055 * A376789 A127013 A117362

Adjacent sequences: A202449 A202450 A202451 * A202453 A202454 A202455

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 19 2011

Status

approved