A202452 - OEIS

%I #16 Feb 18 2020 14:02:41

%S 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,

%T 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,

%U 0,0,144,55,21,8,3,1,0,0,0,0,0,0

%N Lower triangular Fibonacci matrix, by SW antidiagonals.

%H Clark Kimberling, <a href="https://www.fq.math.ca/Papers1/52-3/Kimberling11132013.pdf">Fusion, Fission, and Factors</a>, Fib. Q., 52 (2014), 195-202.

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

%e Northwest corner:

%e 1...0...0...0...0...0...0...0...0

%e 1...1...0...0...0...0...0...0...0

%e 2...1...1...0...0...0...0...0...0

%e 3...2...1...1...0...0...0...0...0

%e 5...3...2...1...1...0...0...0...0

%t n = 12;

%t Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];

%t P = Transpose[Q]; F = P.Q;

%t Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202451 as a sequence *)

%t Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202452 as a sequence *)

%t Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202453 as a sequence *)

%t TableForm[Q]  (* A202451, upper triangular Fibonacci array *)

%t TableForm[P]  (* A202452, lower triangular Fibonacci array *)

%t TableForm[F]  (* A202453, Fibonacci self-fusion matrix *)

%t TableForm[FactorInteger[F]]

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

%K nonn,tabl

%O 1,4

%A _Clark Kimberling_, Dec 19 2011