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A184039
T(n,k) = 1/16 the number of (n+1) X (k+1) 0..3 arrays with all 2 X 2 subblocks having the same four values.
12
16, 28, 28, 49, 40, 49, 91, 61, 61, 91, 169, 103, 82, 103, 169, 325, 181, 124, 124, 181, 325, 625, 337, 202, 166, 202, 337, 625, 1225, 637, 358, 244, 244, 358, 637, 1225, 2401, 1237, 658, 400, 322, 400, 658, 1237, 2401, 4753, 2413, 1258, 700, 478, 478, 700, 1258
OFFSET
1,1
COMMENTS
Table starts
...16...28...49...91..169..325..625.1225.2401.4753..9409.18721.37249.74305
...28...40...61..103..181..337..637.1237.2413.4765..9421.18733.37261.74317
...49...61...82..124..202..358..658.1258.2434.4786..9442.18754.37282.74338
...91..103..124..166..244..400..700.1300.2476.4828..9484.18796.37324.74380
..169..181..202..244..322..478..778.1378.2554.4906..9562.18874.37402.74458
..325..337..358..400..478..634..934.1534.2710.5062..9718.19030.37558.74614
..625..637..658..700..778..934.1234.1834.3010.5362.10018.19330.37858.74914
.1225.1237.1258.1300.1378.1534.1834.2434.3610.5962.10618.19930.38458.75514
.2401.2413.2434.2476.2554.2710.3010.3610.4786.7138.11794.21106.39634.76690
.4753.4765.4786.4828.4906.5062.5362.5962.7138.9490.14146.23458.41986.79042
LINKS
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) = -14 + 9*(2^(n-1) + 2^(k-1)) + 3*(2^(floor((n-1)/2)) + 2^(floor(n/2)) + 2^(floor((k-1)/2)) + 2^(floor(k/2))). (End)
EXAMPLE
Some solutions for 4X3
..0..3..0....3..2..3....3..2..3....1..0..1....2..3..2....3..2..2....3..1..3
..3..2..3....3..3..3....1..3..1....2..1..2....3..2..3....2..1..3....1..2..1
..3..0..3....3..2..3....3..2..3....0..1..0....2..3..2....3..2..2....3..1..3
..2..3..2....3..3..3....1..3..1....1..2..1....2..3..2....2..1..3....2..1..2
PROG
(PARI) T(n, k) = my(m=4, 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
Main diagonal is A184030.
Sequence in context: A300132 A101857 A350302 * A212051 A166595 A280989
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 08 2011
STATUS
approved