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A264745
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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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1
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1, 2, 3, 5, 13, 8, 34, 233, 89, 21, 1597, 75025, 10946, 610, 55, 3524578, 7778742049, 165580141, 514229, 4181, 144, 17167680177565, 83621143489848422977, 37889062373143906, 365435296162, 24157817, 28657, 377, 407305795904080553832073954
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OFFSET
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1,2
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COMMENTS
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The array exhausts, without duplication, the subsequence of A000045 obtained by removing the first two terms {0,1}.
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LINKS
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FORMULA
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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.
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EXAMPLE
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The array begins:
. 1 3 8 21
. 2 13 89 610
. 5 233 10946 514229
. 34 75025 165580141 365435296162
. 1597 7778742049 37889062373143906 184551825793033096366333
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MATHEMATICA
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(* Array: *)
Grid[Table[Fibonacci[2^(n - 1)*(2 k - 1) + 1], {n, 5}, {k, 4}]]
(* Array antidiagonal flattened: *)
Flatten[Table[Fibonacci[2^(n - k)*(2 k - 1) + 1], {n, 7}, {k, n}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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