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A202451 Upper triangular Fibonacci matrix, by SW antidiagonals.

%I A202451 #21 Jan 05 2025 19:51:39
%S A202451 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 A202451 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 A202451 89,0,0,0,0,0,0,1,3,8,21,55,144
%N A202451 Upper triangular Fibonacci matrix, by SW antidiagonals.
%H A202451 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 A202451 Row n consists of n-1 zeros followed by the Fibonacci sequence (1, 1, 2, 3, 5, 8, ...).
%e A202451 Northwest corner:
%e A202451 1...1...2...3...5...8...13...21...34
%e A202451 0...1...1...2...3...5....8...13...21
%e A202451 0...0...1...1...2...3....5....8...13
%e A202451 0...0...0...1...1...2....3....5....8
%t A202451 n = 12;
%t A202451 Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];
%t A202451 P = Transpose[Q]; F = P.Q;
%t A202451 Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202451 as a sequence *)
%t A202451 Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202452 as a sequence *)
%t A202451 Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202453 as a sequence *)
%t A202451 TableForm[Q]  (* A202451, upper triangular Fibonacci matrix *)
%t A202451 TableForm[P]  (* A202452, lower triangular Fibonacci matrix *)
%t A202451 TableForm[F]  (* A202453, Fibonacci self-fusion matrix *)
%t A202451 TableForm[FactorInteger[F]]
%Y A202451 Cf. A000045, A188516, A202452, A202453, A202462.
%K A202451 nonn,tabl
%O A202451 1,6
%A A202451 _Clark Kimberling_, Dec 19 2011