cp's OEIS Frontend

A257068 Number of length 6 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.

%I A257068 #6 Jun 02 2025 11:46:49
%S A257068 4,33,284,729,4096,7353,20249,37893,80545,117649,262144,354756,612724,
%T A257068 882855,1398784,1771561,2985984,3661425,5323339,6888321,9595049,
%U A257068 11390625,16777216,19566096,26006996,31736589,41119756,47045881,64000000,72407025
%N A257068 Number of length 6 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.
%C A257068 Row 6 of A257062
%H A257068 R. H. Hardin, <a href="/A257068/b257068.txt">Table of n, a(n) for n = 1..210</a>
%F A257068 Empirical: a(n) = a(n-1) +6*a(n-6) -6*a(n-7) -15*a(n-12) +15*a(n-13) +20*a(n-18) -20*a(n-19) -15*a(n-24) +15*a(n-25) +6*a(n-30) -6*a(n-31) -a(n-36) +a(n-37)
%F A257068 Empirical for n mod 6 = 0: a(n) = (64/729)*n^6 + (80/243)*n^5 + (40/81)*n^4 + (7/27)*n^3 + (1/36)*n^2
%F A257068 Empirical for n mod 6 = 1: a(n) = (64/729)*n^6 + (104/243)*n^5 + (26/27)*n^4 + (6515/5832)*n^3 + (1181/1944)*n^2 + (161/648)*n + (3197/5832)
%F A257068 Empirical for n mod 6 = 2: a(n) = (64/729)*n^6 + (88/243)*n^5 + (2/3)*n^4 + (2917/5832)*n^3 + (337/972)*n^2 + (50/81)*n - (1091/729)
%F A257068 Empirical for n mod 6 = 3: a(n) = (64/729)*n^6 + (112/243)*n^5 + (8/9)*n^4 + (29/27)*n^3 + (25/36)*n^2 + (1/6)*n + (1/4)
%F A257068 Empirical for n mod 6 = 4: a(n) = (64/729)*n^6 + (64/243)*n^5 + (80/243)*n^4 + (160/729)*n^3 + (20/243)*n^2 + (4/243)*n + (1/729)
%F A257068 Empirical for n mod 6 = 5: a(n) = (64/729)*n^6 + (128/243)*n^5 + (320/243)*n^4 + (1280/729)*n^3 + (320/243)*n^2 + (128/243)*n + (64/729)
%e A257068 Some solutions for n=4
%e A257068 ..4....2....4....2....2....3....3....2....3....4....2....2....3....2....3....3
%e A257068 ..5....4....2....4....1....3....3....2....3....5....1....1....5....4....3....5
%e A257068 ..5....2....4....2....3....3....4....4....3....1....3....5....1....2....2....1
%e A257068 ..2....2....5....2....3....3....2....4....1....4....4....2....5....4....4....3
%e A257068 ..5....5....1....2....1....3....4....4....2....1....4....4....2....4....3....2
%e A257068 ..5....1....4....2....2....3....5....2....3....5....4....4....4....4....1....1
%Y A257068 Cf. A257062
%K A257068 nonn
%O A257068 1,1
%A A257068 _R. H. Hardin_, Apr 15 2015