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Upper triangular Fibonacci matrix, by SW antidiagonals.
6

%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