[seqfan] T(n,k) : F(n)+F(k)

[Ron Hardin]

A problem I passed over but maybe worth mentioning, where T(n,k)=F(n+1)+F(k+1)-1
empirically, as a concrete combinatorial problem

/tmp/ftd
T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, and with new values introduced in order 0 sequentially upwards

Table starts
..1..2..3..5..8..13..21..34..55..89.144.233.377.610..987.1597.2584.4181.6765
..2..3..4..6..9..14..22..35..56..90.145.234.378.611..988.1598.2585.4182.6766
..3..4..5..7.10..15..23..36..57..91.146.235.379.612..989.1599.2586.4183.6767
..5..6..7..9.12..17..25..38..59..93.148.237.381.614..991.1601.2588.4185.6769
..8..9.10.12.15..20..28..41..62..96.151.240.384.617..994.1604.2591.4188.6772
.13.14.15.17.20..25..33..46..67.101.156.245.389.622..999.1609.2596.4193.....
.21.22.23.25.28..33..41..54..75.109.164.253.397.630.1007.1617.2604..........
.34.35.36.38.41..46..54..67..88.122.177.266.410.643.1020.1630...............
.55.56.57.59.62..67..75..88.109.143.198.287.431.664.1041....................
.89.90.91.93.96.101.109.122.143.177.232.321.465.698.........................

All.solutions.for.5X5..
..0..0..1..1..0....0..1..1..0..1....0..1..0..1..1....0..1..0..1..0..
..1..1..0..0..1....1..0..0..1..0....1..0..1..0..0....0..1..0..1..0..
..0..0..1..1..0....0..1..1..0..1....0..1..0..1..1....1..0..1..0..1..
..1..1..0..0..1....1..0..0..1..0....1..0..1..0..0....1..0..1..0..1..
..0..0..1..1..0....0..1..1..0..1....0..1..0..1..1....0..1..0..1..0..
..
..0..1..0..1..0....0..1..0..0..1....0..0..1..0..1....0..1..1..0..0..
..0..1..0..1..0....1..0..1..1..0....1..1..0..1..0....1..0..0..1..1..
..1..0..1..0..1....0..1..0..0..1....0..0..1..0..1....0..1..1..0..0..
..0..1..0..1..0....1..0..1..1..0....1..1..0..1..0....1..0..0..1..1..
..1..0..1..0..1....0..1..0..0..1....0..0..1..0..1....0..1..1..0..0..
..
..0..1..0..1..0....0..1..0..1..0....0..1..0..1..0....0..1..0..1..0..
..1..0..1..0..1....1..0..1..0..1....1..0..1..0..1....1..0..1..0..1..
..0..1..0..1..0....1..0..1..0..1....0..1..0..1..0....0..1..0..1..0..
..1..0..1..0..1....0..1..0..1..0....1..0..1..0..1....0..1..0..1..0..
..0..1..0..1..0....0..1..0..1..0....1..0..1..0..1....1..0..1..0..1..
..
..0..1..0..1..0....0..1..0..1..0....0..0..1..0..0..
..0..1..0..1..0....1..0..1..0..1....1..1..0..1..1..
..1..0..1..0..1....1..0..1..0..1....0..0..1..0..0..
..0..1..0..1..0....0..1..0..1..0....1..1..0..1..1..
..0..1..0..1..0....1..0..1..0..1....0..0..1..0..0..

perhaps related to tiling.
 rhhardin at mindspring.com rhhardin at att.net (either)