A257064 - OEIS

%I #8 Dec 20 2018 15:54:29

%S 2,4,7,9,16,18,27,35,45,49,64,68,84,98,115,121,144,150,173,193,217,

%T 225,256,264,294,320,351,361,400,410,447,479,517,529,576,588,632,670,

%U 715,729,784,798,849,893,945,961,1024,1040,1098,1148,1207,1225,1296,1314,1379

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

%H R. H. Hardin, <a href="/A257064/b257064.txt">Table of n, a(n) for n = 1..210</a>

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

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

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

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

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

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

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

%F 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

%e All solutions for n=4:

%e ..2....4....4....3....3....2....3....2....4

%e ..1....2....4....1....3....2....5....4....5

%Y Row 2 of A257062.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 15 2015