A254827 T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2, 3 or 5

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, 80, 10, 7, 35, 121, 381, 500, 496, 141, 11, 8, 44, 185, 547, 1569, 1557, 1262, 250, 15, 8, 55, 259, 1000, 2644, 6898, 5316, 3476, 432, 19, 9, 60, 376, 1604, 5780, 13504, 31005

Offset

1,2

Comments

Table starts

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

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

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

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

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

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

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

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

.15.432.10400..69536..621384.1827707..6724852..17661777..53722219.107630792

.19.811.30718.248613.2737649.8901990.37283903.111266547.391034008.853525572

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

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

k=1: [linear recurrence of order 22]

k=2: [order 22]

k=3: [order 22]

k=4: [order 19]

k=5: [order 16]

k=6: [order 22]

k=7: [order 22]

Empirical for row n:

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

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

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)

Example

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

Crossrefs

Sequence in context: A317449 A222310 A294033 * A193862 A258631 A254947

Adjacent sequences: A254824 A254825 A254826 * A254828 A254829 A254830

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 08 2015

Status

approved