This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A257069 #6 Jun 02 2025 11:46:56 %S A257069 4,59,713,2187,16384,33048,106056,217603,523733,823543,2097152, %T A257069 3014848,5663370,8603223,14688611,19487171,35831808,45765000,70508164, %U A257069 94687187,139133363,170859375,268435456,322831872,448523376,563223955,760729349 %N A257069 Number of length 7 1..(n+1) arrays with every leading partial sum divisible by 2 or 3. %C A257069 Row 7 of A257062 %H A257069 R. H. Hardin, <a href="/A257069/b257069.txt">Table of n, a(n) for n = 1..210</a> %F A257069 Empirical: a(n) = a(n-1) +7*a(n-6) -7*a(n-7) -21*a(n-12) +21*a(n-13) +35*a(n-18) -35*a(n-19) -35*a(n-24) +35*a(n-25) +21*a(n-30) -21*a(n-31) -7*a(n-36) +7*a(n-37) +a(n-42) -a(n-43) %F A257069 Empirical for n mod 6 = 0: a(n) = (128/2187)*n^7 + (64/243)*n^6 + (40/81)*n^5 + (32/81)*n^4 + (1/9)*n^3 %F A257069 Empirical for n mod 6 = 1: a(n) = (128/2187)*n^7 + (736/2187)*n^6 + (644/729)*n^5 + (2765/2187)*n^4 + (17999/17496)*n^3 + (2885/5832)*n^2 + (9121/17496)*n - (10279/17496) %F A257069 Empirical for n mod 6 = 2: a(n) = (128/2187)*n^7 + (608/2187)*n^6 + (428/729)*n^5 + (1321/2187)*n^4 + (4141/8748)*n^3 + (775/1458)*n^2 - (1534/2187)*n + (1649/2187) %F A257069 Empirical for n mod 6 = 3: a(n) = (128/2187)*n^7 + (256/729)*n^6 + (200/243)*n^5 + (32/27)*n^4 + (28/27)*n^3 + (17/36)*n^2 + (1/3)*n - (1/4) %F A257069 Empirical for n mod 6 = 4: a(n) = (128/2187)*n^7 + (448/2187)*n^6 + (224/729)*n^5 + (560/2187)*n^4 + (280/2187)*n^3 + (28/729)*n^2 + (14/2187)*n + (1/2187) %F A257069 Empirical for n mod 6 = 5: a(n) = (128/2187)*n^7 + (896/2187)*n^6 + (896/729)*n^5 + (4480/2187)*n^4 + (4480/2187)*n^3 + (896/729)*n^2 + (896/2187)*n + (128/2187) %e A257069 Some solutions for n=4 %e A257069 ..4....2....2....2....4....3....3....2....3....3....2....4....3....4....2....2 %e A257069 ..2....2....1....2....2....5....3....1....3....5....4....4....3....4....4....4 %e A257069 ..4....2....3....4....3....2....3....1....3....4....2....1....4....1....2....4 %e A257069 ..2....3....3....2....3....5....1....5....5....3....2....1....2....3....4....2 %e A257069 ..3....1....1....5....4....1....5....5....1....3....5....2....3....3....3....2 %e A257069 ..1....2....4....3....4....2....3....2....1....3....3....4....3....3....1....4 %e A257069 ..5....4....2....2....2....2....4....2....4....3....4....5....2....2....2....3 %Y A257069 Cf. A257062 %K A257069 nonn %O A257069 1,1 %A A257069 _R. H. Hardin_, Apr 15 2015