A254828 Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3 or 5.

1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 31, 32, 33, 34, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 44, 45, 46, 47, 48, 49, 49, 50, 51, 52, 52, 53, 53, 54, 55, 56, 56

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + x + x^2 + x^3 + x^4 + x^6 + x^7 + x^8 + x^10 + x^12 + x^13 + x^14 + x^16 + x^18 + x^19 + x^20 + x^22 + x^23 + x^24 + x^25 + x^26 + x^28) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)*(1 + x - x^3 - x^4 - x^5 + x^7 + x^8)). - Colin Barker, Dec 18 2018

Example

All solutions for n=4:
..2....5....3....4

Crossrefs

Row 1 of A254827.

Sequence in context: A138366 A065515 A070545 * A091863 A163296 A247971

Adjacent sequences: A254825 A254826 A254827 * A254829 A254830 A254831

Keyword

nonn

Author

R. H. Hardin, Feb 08 2015

Status

approved