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A202452 Lower triangular Fibonacci matrix, by SW antidiagonals.

%I A202452 #17 Jan 05 2025 19:51:39
%S A202452 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 A202452 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 A202452 0,0,144,55,21,8,3,1,0,0,0,0,0,0
%N A202452 Lower triangular Fibonacci matrix, by SW antidiagonals.
%H A202452 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/52-3/Kimberling11132013.pdf">Fusion, Fission, and Factors</a>, Fib. Q., 52 (2014), 195-202.
%F A202452 Column n consists of n-1 zeros followed by the Fibonacci sequence (1,1,2,3,5,8,...).
%e A202452 Northwest corner:
%e A202452 1...0...0...0...0...0...0...0...0
%e A202452 1...1...0...0...0...0...0...0...0
%e A202452 2...1...1...0...0...0...0...0...0
%e A202452 3...2...1...1...0...0...0...0...0
%e A202452 5...3...2...1...1...0...0...0...0
%t A202452 n = 12;
%t A202452 Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];
%t A202452 P = Transpose[Q]; F = P.Q;
%t A202452 Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202451 as a sequence *)
%t A202452 Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202452 as a sequence *)
%t A202452 Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202453 as a sequence *)
%t A202452 TableForm[Q]  (* A202451, upper triangular Fibonacci array *)
%t A202452 TableForm[P]  (* A202452, lower triangular Fibonacci array *)
%t A202452 TableForm[F]  (* A202453, Fibonacci self-fusion matrix *)
%t A202452 TableForm[FactorInteger[F]]
%Y A202452 Cf. A202451, A202453, A202462, A188516, A000045.
%K A202452 nonn,tabl
%O A202452 1,4
%A A202452 _Clark Kimberling_, Dec 19 2011