OFFSET
1,1
COMMENTS
Table starts
....9...15...25...45...81..153..289..561.1089.2145.4225..8385.16641.33153.66049
...15...21...31...51...87..159..295..567.1095.2151.4231..8391.16647.33159.66055
...25...31...41...61...97..169..305..577.1105.2161.4241..8401.16657.33169.66065
...45...51...61...81..117..189..325..597.1125.2181.4261..8421.16677.33189.66085
...81...87...97..117..153..225..361..633.1161.2217.4297..8457.16713.33225.66121
..153..159..169..189..225..297..433..705.1233.2289.4369..8529.16785.33297.66193
..289..295..305..325..361..433..569..841.1369.2425.4505..8665.16921.33433.66329
..561..567..577..597..633..705..841.1113.1641.2697.4777..8937.17193.33705.66601
.1089.1095.1105.1125.1161.1233.1369.1641.2169.3225.5305..9465.17721.34233.67129
.2145.2151.2161.2181.2217.2289.2425.2697.3225.4281.6361.10521.18777.35289.68185
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..391
FORMULA
Empirical, for all rows and columns: a(n)=3*a(n-1)-6*a(n-3)+4*a(n-4).
From Andrew Howroyd, Mar 09 2024: (Start)
The above empirical formula is correct.
T(n,k) = -7 + 4*(2^(n-1) + 2^(k-1)) + 2*(2^(floor((n-1)/2)) + 2^(floor(n/2)) + 2^(floor((k-1)/2)) + 2^(floor(k/2))). (End)
EXAMPLE
Some solutions for 6X5
..0..1..0..1..0....1..2..1..2..1....1..2..1..2..1....2..1..2..2..2
..0..1..0..1..0....1..2..1..2..1....1..0..1..0..1....0..2..0..1..0
..1..0..1..0..1....2..1..2..1..2....1..2..1..2..1....2..1..2..2..2
..0..1..0..1..0....1..2..1..2..1....1..0..1..0..1....0..2..0..1..0
..0..1..0..1..0....1..2..1..2..1....2..1..2..1..2....2..1..2..2..2
..1..0..1..0..1....2..1..2..1..2....0..1..0..1..0....0..2..0..1..0
PROG
(PARI) T(n, k) = my(m=3, b=t->2^t-1); m^2 + (m-1)^2*(b(n-1) + b(k-1)) + (m-1)*(b((n-1)\2) + b(n\2) + b((k-1)\2) + b(k\2)) \\ Andrew Howroyd, Mar 09 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 08 2011
STATUS
approved