A257064 Number of length 2 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.

2, 4, 7, 9, 16, 18, 27, 35, 45, 49, 64, 68, 84, 98, 115, 121, 144, 150, 173, 193, 217, 225, 256, 264, 294, 320, 351, 361, 400, 410, 447, 479, 517, 529, 576, 588, 632, 670, 715, 729, 784, 798, 849, 893, 945, 961, 1024, 1040, 1098, 1148, 1207, 1225, 1296, 1314, 1379

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-6) - 2*a(n-7) - a(n-12) + a(n-13).

Empirical for n mod 6 = 0: a(n) = (4/9)*n^2 + (1/3)*n

Empirical for n mod 6 = 1: a(n) = (4/9)*n^2 + (11/18)*n + (17/18)

Empirical for n mod 6 = 2: a(n) = (4/9)*n^2 + (13/18)*n + (7/9)

Empirical for n mod 6 = 3: a(n) = (4/9)*n^2 + 1*n

Empirical for n mod 6 = 4: a(n) = (4/9)*n^2 + (4/9)*n + (1/9)

Empirical for n mod 6 = 5: a(n) = (4/9)*n^2 + (8/9)*n + (4/9).

Empirical g.f.: x*(2 + 2*x + 3*x^2 + 2*x^3 + 7*x^4 + 2*x^5 + 5*x^6 + 4*x^7 + 4*x^8 + x^10) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2). - Colin Barker, Dec 20 2018

Example

All solutions for n=4:
..2....4....4....3....3....2....3....2....4
..1....2....4....1....3....2....5....4....5

Crossrefs

Row 2 of A257062.

Sequence in context: A097433 A308758 A110078 * A085800 A155190 A333317

Adjacent sequences: A257061 A257062 A257063 * A257065 A257066 A257067

Keyword

nonn

Author

R. H. Hardin, Apr 15 2015

Status

approved