A264745 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.

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

Offset

1,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..78

Formula

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

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

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.

Example

The array begins:
.     1           3                  8                        21
.     2          13                 89                       610
.     5         233              10946                    514229
.    34       75025          165580141              365435296162
.  1597  7778742049  37889062373143906  184551825793033096366333

Mathematica

(* 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}]]

Crossrefs

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

Cf. A192222 (column 1).

Cf. A000045, A001511, A001566, A003602, A054582

Sequence in context: A061488 A236394 A111239 * A251414 A145343 A058592

Adjacent sequences: A264742 A264743 A264744 * A264746 A264747 A264748

Keyword

nonn,tabl

Author

L. Edson Jeffery, Nov 23 2015

Status

approved