A097351 -id:A097351

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A097352

Rectangular array T(n,k) by antidiagonals; rows are generalized Fibonacci sequences and every pair (i,j) satisfying 1 <= i < j occurs exactly once.

+10
1

1, 1, 1, 2, 3, 2, 3, 4, 2, 1, 5, 7, 4, 4, 1, 8, 11, 6, 5, 5, 3, 13, 18, 10, 9, 6, 3, 1, 21, 29, 16, 14, 11, 6, 6, 2, 34, 47, 26, 23, 17, 9, 7, 5, 1, 55, 76, 42, 37, 28, 15, 13, 7, 7, 2, 89, 123, 68, 60, 45, 24, 20, 12, 8, 6, 4, 144, 199, 110, 97, 73, 39, 33, 19, 15, 8, 4, 1, 253, 322

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

In every row, the limiting ratio of consecutive terms is tau.

LINKS

Table of n, a(n) for n=1..80.

FORMULA

Recurrence for row n: T(n, k)=T(n, k-1)+T(n, k-2). Each row after the first begins with lexically least pair not in previous rows.

EXAMPLE

Northwest corner:

1 1 2 3 5

1 3 4 7 11

2 2 4 6 10

1 4 5 9 14

1 5 6 11 17

CROSSREFS

Cf. A000045, A097351.

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2004

STATUS

approved

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