%I #20 Feb 18 2020 18:34:42
%S 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,
%T 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,
%U 89,0,0,0,0,0,0,1,3,8,21,55,144
%N Upper 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 Row n consists of n-1 zeros followed by the Fibonacci sequence (1, 1, 2, 3, 5, 8, ...).
%e Northwest corner:
%e 1...1...2...3...5...8...13...21...34
%e 0...1...1...2...3...5....8...13...21
%e 0...0...1...1...2...3....5....8...13
%e 0...0...0...1...1...2....3....5....8
%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 matrix *)
%t TableForm[P] (* A202452, lower triangular Fibonacci matrix *)
%t TableForm[F] (* A202453, Fibonacci self-fusion matrix *)
%t TableForm[FactorInteger[F]]
%Y Cf. A000045, A188516, A202452, A202453, A202462.
%K nonn,tabl
%O 1,6
%A _Clark Kimberling_, Dec 19 2011