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A202451 Upper triangular Fibonacci matrix, by SW antidiagonals. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)