A257068 Number of length 6 1..(n+1) arrays with every leading partial sum divisible by 2 or 3

4, 33, 284, 729, 4096, 7353, 20249, 37893, 80545, 117649, 262144, 354756, 612724, 882855, 1398784, 1771561, 2985984, 3661425, 5323339, 6888321, 9595049, 11390625, 16777216, 19566096, 26006996, 31736589, 41119756, 47045881, 64000000, 72407025

Offset

1,1

Comments

Row 6 of A257062

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +6*a(n-6) -6*a(n-7) -15*a(n-12) +15*a(n-13) +20*a(n-18) -20*a(n-19) -15*a(n-24) +15*a(n-25) +6*a(n-30) -6*a(n-31) -a(n-36) +a(n-37)

Empirical for n mod 6 = 0: a(n) = (64/729)*n^6 + (80/243)*n^5 + (40/81)*n^4 + (7/27)*n^3 + (1/36)*n^2

Empirical for n mod 6 = 1: a(n) = (64/729)*n^6 + (104/243)*n^5 + (26/27)*n^4 + (6515/5832)*n^3 + (1181/1944)*n^2 + (161/648)*n + (3197/5832)

Empirical for n mod 6 = 2: a(n) = (64/729)*n^6 + (88/243)*n^5 + (2/3)*n^4 + (2917/5832)*n^3 + (337/972)*n^2 + (50/81)*n - (1091/729)

Empirical for n mod 6 = 3: a(n) = (64/729)*n^6 + (112/243)*n^5 + (8/9)*n^4 + (29/27)*n^3 + (25/36)*n^2 + (1/6)*n + (1/4)

Empirical for n mod 6 = 4: a(n) = (64/729)*n^6 + (64/243)*n^5 + (80/243)*n^4 + (160/729)*n^3 + (20/243)*n^2 + (4/243)*n + (1/729)

Empirical for n mod 6 = 5: a(n) = (64/729)*n^6 + (128/243)*n^5 + (320/243)*n^4 + (1280/729)*n^3 + (320/243)*n^2 + (128/243)*n + (64/729)

Example

Some solutions for n=4
..4....2....4....2....2....3....3....2....3....4....2....2....3....2....3....3
..5....4....2....4....1....3....3....2....3....5....1....1....5....4....3....5
..5....2....4....2....3....3....4....4....3....1....3....5....1....2....2....1
..2....2....5....2....3....3....2....4....1....4....4....2....5....4....4....3
..5....5....1....2....1....3....4....4....2....1....4....4....2....4....3....2
..5....1....4....2....2....3....5....2....3....5....4....4....4....4....1....1

Crossrefs

Cf. A257062

Sequence in context: A203212 A041024 A088317 * A246806 A202765 A264830

Adjacent sequences: A257065 A257066 A257067 * A257069 A257070 A257071

Keyword

nonn

Author

R. H. Hardin, Apr 15 2015

Status

approved