A184040 -id:A184040 - cp's OEIS frontend

A184048 T(n,k) = 1/9 the number of (n+1) X (k+1) 0..2 arrays with all 2 X 2 subblocks having the same four values.

9, 15, 15, 25, 21, 25, 45, 31, 31, 45, 81, 51, 41, 51, 81, 153, 87, 61, 61, 87, 153, 289, 159, 97, 81, 97, 159, 289, 561, 295, 169, 117, 117, 169, 295, 561, 1089, 567, 305, 189, 153, 189, 305, 567, 1089, 2145, 1095, 577, 325, 225, 225, 325, 577, 1095, 2145, 4225, 2151

Offset: 1

R. H. Hardin, Jan 08 2011

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

			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

R. H. Hardin, Table of n, a(n) for n = 1..391

Columns 1..8 are A183978(n+2), A184041, A184042, A184043, A184044, A184045, A184046, A184047.
Main diagonal is A184040.
Cf. A183986, A184039.

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

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)

cp's OEIS Frontend

A184048 T(n,k) = 1/9 the number of (n+1) X (k+1) 0..2 arrays with all 2 X 2 subblocks having the same four values.

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