A202502 - OEIS

%I #16 Feb 19 2020 07:24:44

%S 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 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 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 Modified lower triangular Fibonacci matrix, by antidiagonals.

%C 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 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.

%e Northwest corner:

%e 1...0...0...0...0...0...0...0...0

%e 2...1...0...0...0...0...0...0...0

%e 3...2...1...0...0...0...0...0...0

%e 5...3...2...1...1...0...0...0...0

%e 8...5...3...2...1...1...0...0...0

%t n = 14;

%t Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];

%t Qt = Transpose[Q]; P1 = Qt - IdentityMatrix[n];

%t P = P1[[Range[2, n], Range[1, n]]];

%t F = P.Q;

%t Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202502 as a sequence *)

%t Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202451 as a sequence *)

%t Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202503 as a sequence *)

%t TableForm[P]  (* A202502, modified lower triangular Fibonacci matrix *)

%t TableForm[Q] (* A202451, upper tri. Fibonacci matrix *)

%t TableForm[F] (* A202503, Fibonacci self-fission matrix *)

%Y Cf. A202503, A202451, A202452, A202453, A000045.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Dec 20 2011