login
T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2, 3 or 5
15

%I #4 Feb 08 2015 10:28:49

%S 1,2,2,3,6,4,4,10,13,5,5,16,30,26,6,5,23,54,79,48,9,6,26,95,166,197,

%T 80,10,7,35,121,381,500,496,141,11,8,44,185,547,1569,1557,1262,250,15,

%U 8,55,259,1000,2644,6898,5316,3476,432,19,9,60,376,1604,5780,13504,31005

%N T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2, 3 or 5

%C Table starts

%C ..1...2.....3......4.......5.......5........6.........7.........8.........8

%C ..2...6....10.....16......23......26.......35........44........55........60

%C ..4..13....30.....54......95.....121......185.......259.......376.......450

%C ..5..26....79....166.....381.....547.....1000......1604......2711......3568

%C ..6..48...197....500....1569....2644.....5780.....10521.....20196.....28905

%C ..9..80...496...1557....6898...13504....34624.....70093....148847....228892

%C .10.141..1262...5316...31005...69858...207232....455349...1064100...1766942

%C .11.250..3476..19292..138809..361448..1201694...2853488...7510362..13668349

%C .15.432.10400..69536..621384.1827707..6724852..17661777..53722219.107630792

%C .19.811.30718.248613.2737649.8901990.37283903.111266547.391034008.853525572

%H R. H. Hardin, <a href="/A254827/b254827.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for column k (variable recurrence order appears to have period k=30):

%F k=1: [linear recurrence of order 22]

%F k=2: [order 22]

%F k=3: [order 22]

%F k=4: [order 19]

%F k=5: [order 16]

%F k=6: [order 22]

%F k=7: [order 22]

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-30) -a(n-31)

%F n=2: a(n) = a(n-1) +2*a(n-30) -2*a(n-31) -a(n-60) +a(n-61)

%F n=3: a(n) = a(n-1) +3*a(n-30) -3*a(n-31) -3*a(n-60) +3*a(n-61) +a(n-90) -a(n-91)

%e Some solutions for n=4 k=4

%e ..3....2....3....2....2....5....2....3....2....4....3....3....3....4....5....2

%e ..1....1....2....2....1....1....1....5....2....1....5....2....5....1....3....4

%e ..2....1....1....2....5....3....5....2....4....3....1....3....1....5....2....2

%e ..4....5....4....3....2....3....1....4....1....1....1....2....5....2....2....2

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 08 2015