A257063 Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.

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

Offset: 1

Author

R. H. Hardin, Apr 15 2015

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 1 of A257062.

Formula

Empirical: a(n) = a(n-1) + a(n-6) - a(n-7).

Empirical for n mod 6 = 0: a(n) = (2/3)*n

Empirical for n mod 6 = 1: a(n) = (2/3)*n + (1/3)

Empirical for n mod 6 = 2: a(n) = (2/3)*n + (2/3)

Empirical for n mod 6 = 3: a(n) = (2/3)*n + 1

Empirical for n mod 6 = 4: a(n) = (2/3)*n + (1/3)

Empirical for n mod 6 = 5: a(n) = (2/3)*n + (2/3).

Empirical g.f.: x*(1 + x + x^2 + x^4) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)). - Colin Barker, Dec 20 2018