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 A249002 #11 Nov 09 2018 21:54:27 %S A249002 30,190,820,2540,6450,13990,27740,50260,86030,139450,217320,325940, %T A249002 475630,674650,937020,1274160,1703970,2240850,2908260,3723400,4715230, %U A249002 5905430,7328400,9009880,10991870,13303750,15994820,19100260,22676370 %N A249002 Number of length 1+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two. %H A249002 R. H. Hardin, <a href="/A249002/b249002.txt">Table of n, a(n) for n = 1..209</a> %F A249002 Empirical: a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 5*a(n-4) - 3*a(n-5) + 6*a(n-6) + 6*a(n-7) - 3*a(n-8) - 5*a(n-9) - a(n-10) + 3*a(n-11) + a(n-12) - a(n-13). %F A249002 Empirical for n mod 6 = 0: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (55/6)*n^2 + (47/3)*n %F A249002 Empirical for n mod 6 = 1: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (65/12)*n^2 + (86/9)*n + (565/72) %F A249002 Empirical for n mod 6 = 2: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (55/6)*n^2 + (181/9)*n - (20/9) %F A249002 Empirical for n mod 6 = 3: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (65/12)*n^2 + (2/3)*n + (205/8) %F A249002 Empirical for n mod 6 = 4: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (55/6)*n^2 + (221/9)*n - (160/9) %F A249002 Empirical for n mod 6 = 5: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (65/12)*n^2 + (46/9)*n + (1685/72). %F A249002 Empirical g.f.: 10*x*(3 + 16*x + 54*x^2 + 118*x^3 + 179*x^4 + 178*x^5 + 143*x^6 + 84*x^7 + 44*x^8 + 24*x^9 + 21*x^10) / ((1 - x)^6*(1 + x)^3*(1 + x + x^2)^2). - _Colin Barker_, Nov 09 2018 %e A249002 Some solutions for n=6: %e A249002 6 2 5 5 0 5 4 4 3 2 2 6 3 4 0 0 %e A249002 4 3 4 5 3 1 5 6 1 2 1 6 4 6 1 3 %e A249002 1 1 6 4 5 6 5 2 0 1 6 6 0 2 1 1 %e A249002 1 5 5 1 1 4 5 6 2 1 0 6 3 6 0 4 %e A249002 3 1 0 1 0 3 1 1 2 2 5 2 4 0 5 4 %Y A249002 Row 1 of A249001. %K A249002 nonn %O A249002 1,1 %A A249002 _R. H. Hardin_, Oct 18 2014