

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
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OFFSET

1,4


REFERENCES

C. Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195202.


LINKS

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


FORMULA

Column n consists of n1 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 selffusion 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



