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Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = Fibonacci(2^(n-1)*(2*k-1) + 1), n,k >= 1.
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%I #13 Dec 03 2015 04:27:40

%S 1,2,3,5,13,8,34,233,89,21,1597,75025,10946,610,55,3524578,7778742049,

%T 165580141,514229,4181,144,17167680177565,83621143489848422977,

%U 37889062373143906,365435296162,24157817,28657,377,407305795904080553832073954

%N Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = Fibonacci(2^(n-1)*(2*k-1) + 1), n,k >= 1.

%C The array exhausts, without duplication, the subsequence of A000045 obtained by removing the first two terms {0,1}.

%H G. C. Greubel, <a href="/A264745/b264745.txt">Table of n, a(n) for n = 1..78</a>

%F A(n,k) = A000045(A054582(n-1,k-1) + 1).

%F A(A001511(m),A003602(m)) = A000045(m+1), m >= 1.

%F Conjectured g.f. for row n: x*(A000045(2^(n-1)+1) - A000045(2^(n-1)-1)*x)/(1 - A001566(n)*x + x^2), n >= 1.

%e The array begins:

%e . 1 3 8 21

%e . 2 13 89 610

%e . 5 233 10946 514229

%e . 34 75025 165580141 365435296162

%e . 1597 7778742049 37889062373143906 184551825793033096366333

%t (* Array: *)

%t Grid[Table[Fibonacci[2^(n - 1)*(2 k - 1) + 1], {n, 5}, {k, 4}]]

%t (* Array antidiagonal flattened: *)

%t Flatten[Table[Fibonacci[2^(n - k)*(2 k - 1) + 1], {n, 7}, {k, n}]]

%Y Cf. A001906, A033891 (rows 1--2).

%Y Cf. A192222 (column 1).

%Y Cf. A000045, A001511, A001566, A003602, A054582

%K nonn,tabl

%O 1,2

%A _L. Edson Jeffery_, Nov 23 2015