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 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. 1
 30, 190, 820, 2540, 6450, 13990, 27740, 50260, 86030, 139450, 217320, 325940, 475630, 674650, 937020, 1274160, 1703970, 2240850, 2908260, 3723400, 4715230, 5905430, 7328400, 9009880, 10991870, 13303750, 15994820, 19100260, 22676370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. H. Hardin, Table of n, a(n) for n = 1..209 FORMULA 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). 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 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) 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) 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) 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) 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). 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 EXAMPLE Some solutions for n=6: 6 2 5 5 0 5 4 4 3 2 2 6 3 4 0 0 4 3 4 5 3 1 5 6 1 2 1 6 4 6 1 3 1 1 6 4 5 6 5 2 0 1 6 6 0 2 1 1 1 5 5 1 1 4 5 6 2 1 0 6 3 6 0 4 3 1 0 1 0 3 1 1 2 2 5 2 4 0 5 4 CROSSREFS Row 1 of A249001. Sequence in context: A265037 A249001 A249466 * A249467 A309924 A120339 Adjacent sequences: A248999 A249000 A249001 * A249003 A249004 A249005 KEYWORD nonn AUTHOR R. H. Hardin, Oct 18 2014 STATUS approved

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Last modified September 9 13:08 EDT 2024. Contains 375764 sequences. (Running on oeis4.)