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A202502 Modified lower triangular Fibonacci matrix, by antidiagonals.

%I A202502 #17 Jan 05 2025 19:51:39
%S A202502 1,0,2,0,1,3,0,0,2,5,0,0,1,3,8,0,0,0,2,5,13,0,0,0,1,3,8,21,0,0,0,0,2,
%T A202502 5,13,34,0,0,0,0,1,3,8,21,55,0,0,0,0,0,2,5,13,34,89,0,0,0,0,0,1,3,8,
%U A202502 21,55,144,0,0,0,0,0,0,2,5,13,34,89,233,0,0,0,0,0,0,1,3,8,21,55
%N A202502 Modified lower triangular Fibonacci matrix, by antidiagonals.
%C A202502 This matrix, P, is used to form the Fibonacci self-fission matrix as the product P*Q, where Q is the upper triangular Fibonacci matrix, A202451.  To form P, delete the main diagonal of the transpose of Q.
%H A202502 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.
%e A202502 Northwest corner:
%e A202502 1...0...0...0...0...0...0...0...0
%e A202502 2...1...0...0...0...0...0...0...0
%e A202502 3...2...1...0...0...0...0...0...0
%e A202502 5...3...2...1...1...0...0...0...0
%e A202502 8...5...3...2...1...1...0...0...0
%t A202502 n = 14;
%t A202502 Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];
%t A202502 Qt = Transpose[Q]; P1 = Qt - IdentityMatrix[n];
%t A202502 P = P1[[Range[2, n], Range[1, n]]];
%t A202502 F = P.Q;
%t A202502 Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202502 as a sequence *)
%t A202502 Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202451 as a sequence *)
%t A202502 Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202503 as a sequence *)
%t A202502 TableForm[P]  (* A202502, modified lower triangular Fibonacci matrix *)
%t A202502 TableForm[Q] (* A202451, upper tri. Fibonacci matrix *)
%t A202502 TableForm[F] (* A202503, Fibonacci self-fission matrix *)
%Y A202502 Cf. A202503, A202451, A202452, A202453, A000045.
%K A202502 nonn,tabl
%O A202502 1,3
%A A202502 _Clark Kimberling_, Dec 20 2011