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A202452 Lower triangular Fibonacci matrix, by SW antidiagonals. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

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

LINKS

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

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 * A127013 A117362 A247492

Adjacent sequences:  A202449 A202450 A202451 * A202453 A202454 A202455

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 19 2011

STATUS

approved

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Last modified December 14 14:37 EST 2018. Contains 318098 sequences. (Running on oeis4.)