A254820 Number of length n 1..(1+1) arrays with every leading partial sum divisible by 2, 3 or 5.

1, 2, 4, 5, 6, 9, 10, 11, 15, 19, 21, 26, 35, 48, 75, 120, 166, 203, 262, 395, 613, 879, 1174, 1502, 1849, 2237, 2738, 3364, 4104, 5107, 6727, 9500, 14046, 20588, 28704, 38517, 52473, 74917, 109037, 154672, 209449, 271287, 340040, 418493, 512101, 627661

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-15) + 9*a(n-16) + 32*a(n-17) + 58*a(n-18) + 58*a(n-19) + 32*a(n-20) + 9*a(n-21) + a(n-22).

Empirical g.f.: x*(1 + x)*(1 + x + 3*x^2 + 2*x^3 + 4*x^4 + 5*x^5 + 5*x^6 + 6*x^7 + 9*x^8 + 10*x^9 + 11*x^10 + 15*x^11 + 20*x^12 + 28*x^13 + 47*x^14 + 72*x^15 + 83*x^16 + 66*x^17 + 33*x^18 + 9*x^19 + x^20) / (1 - x^15 - 9*x^16 - 32*x^17 - 58*x^18 - 58*x^19 - 32*x^20 - 9*x^21 - x^22). - Colin Barker, Dec 18 2018

Example

All solutions for n=4:
..2....2....2....2....2
..1....1....2....1....2
..2....1....1....1....2
..1....2....1....1....2

Crossrefs

Column 1 of A254827.

Sequence in context: A361936 A069470 A376423 * A332570 A047435 A331085

Adjacent sequences: A254817 A254818 A254819 * A254821 A254822 A254823

Keyword

nonn

Author

R. H. Hardin, Feb 08 2015

Status

approved