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A257069
Number of length 7 1..(n+1) arrays with every leading partial sum divisible by 2 or 3
1
4, 59, 713, 2187, 16384, 33048, 106056, 217603, 523733, 823543, 2097152, 3014848, 5663370, 8603223, 14688611, 19487171, 35831808, 45765000, 70508164, 94687187, 139133363, 170859375, 268435456, 322831872, 448523376, 563223955, 760729349
OFFSET
1,1
COMMENTS
Row 7 of A257062
LINKS
FORMULA
Empirical: a(n) = a(n-1) +7*a(n-6) -7*a(n-7) -21*a(n-12) +21*a(n-13) +35*a(n-18) -35*a(n-19) -35*a(n-24) +35*a(n-25) +21*a(n-30) -21*a(n-31) -7*a(n-36) +7*a(n-37) +a(n-42) -a(n-43)
Empirical for n mod 6 = 0: a(n) = (128/2187)*n^7 + (64/243)*n^6 + (40/81)*n^5 + (32/81)*n^4 + (1/9)*n^3
Empirical for n mod 6 = 1: a(n) = (128/2187)*n^7 + (736/2187)*n^6 + (644/729)*n^5 + (2765/2187)*n^4 + (17999/17496)*n^3 + (2885/5832)*n^2 + (9121/17496)*n - (10279/17496)
Empirical for n mod 6 = 2: a(n) = (128/2187)*n^7 + (608/2187)*n^6 + (428/729)*n^5 + (1321/2187)*n^4 + (4141/8748)*n^3 + (775/1458)*n^2 - (1534/2187)*n + (1649/2187)
Empirical for n mod 6 = 3: a(n) = (128/2187)*n^7 + (256/729)*n^6 + (200/243)*n^5 + (32/27)*n^4 + (28/27)*n^3 + (17/36)*n^2 + (1/3)*n - (1/4)
Empirical for n mod 6 = 4: a(n) = (128/2187)*n^7 + (448/2187)*n^6 + (224/729)*n^5 + (560/2187)*n^4 + (280/2187)*n^3 + (28/729)*n^2 + (14/2187)*n + (1/2187)
Empirical for n mod 6 = 5: a(n) = (128/2187)*n^7 + (896/2187)*n^6 + (896/729)*n^5 + (4480/2187)*n^4 + (4480/2187)*n^3 + (896/729)*n^2 + (896/2187)*n + (128/2187)
EXAMPLE
Some solutions for n=4
..4....2....2....2....4....3....3....2....3....3....2....4....3....4....2....2
..2....2....1....2....2....5....3....1....3....5....4....4....3....4....4....4
..4....2....3....4....3....2....3....1....3....4....2....1....4....1....2....4
..2....3....3....2....3....5....1....5....5....3....2....1....2....3....4....2
..3....1....1....5....4....1....5....5....1....3....5....2....3....3....3....2
..1....2....4....3....4....2....3....2....1....3....3....4....3....3....1....4
..5....4....2....2....2....2....4....2....4....3....4....5....2....2....2....3
CROSSREFS
Sequence in context: A113251 A183462 A093597 * A199107 A280668 A198508
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 15 2015
STATUS
approved