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

1,6

Links

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

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

Formula

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

Example

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

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]]

Crossrefs

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

Sequence in context: A122950 A116489 A166373 * A238727 A056885 A029373

Adjacent sequences: A202448 A202449 A202450 * A202452 A202453 A202454

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 19 2011

Status

approved