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.

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

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.

Sequence in context: A257396 A293519 A237582 * A076050 A130799 A243519

Adjacent sequences: A097349 A097350 A097351 * A097353 A097354 A097355

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2004

Status

approved