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 A249467 Number of length 1+4 0..n arrays with no five consecutive terms having four times any element equal to the sum of the remaining four. 1
 30, 190, 860, 2640, 6730, 14730, 29060, 52900, 90390, 146610, 228000, 342120, 498030, 706270, 979100, 1330440, 1776250, 2334330, 3024740, 3869740, 4893990, 6124530, 7591200, 9326400, 11365470, 13746670, 16511420, 19704240, 23373130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 4*a(n-7) + 5*a(n-8) - 6*a(n-9) + 4*a(n-10) - a(n-11). Also a polynomial of degree 5 plus a constant pseudonomial with period 12: Empirical for n mod 12 = 0: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n Empirical for n mod 12 = 1: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (65/12) Empirical for n mod 12 = 2: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (20/3) Empirical for n mod 12 = 3: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (35/4) Empirical for n mod 12 = 4: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (40/3) Empirical for n mod 12 = 5: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (145/12) Empirical for n mod 12 = 6: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n Empirical for n mod 12 = 7: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (55/12) Empirical for n mod 12 = 8: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (20/3) Empirical for n mod 12 = 9: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (75/4) Empirical for n mod 12 = 10: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (40/3) Empirical for n mod 12 = 11: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (25/12). Empirical g.f.: 10*x*(3 + 7*x + 28*x^2 + 19*x^3 + 50*x^4 + 5*x^5 + 32*x^6 - 3*x^7 + 3*x^8) / ((1 - x)^6*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 09 2018 EXAMPLE Some solutions for n=6: 2 4 0 0 6 6 0 6 4 0 1 4 2 4 2 5 3 3 2 6 5 0 1 3 6 0 3 6 1 3 4 1 4 6 0 6 4 0 5 6 0 6 4 0 5 3 6 2 3 0 3 1 2 4 5 0 0 0 4 5 6 1 0 5 5 0 2 2 0 6 6 5 3 1 5 6 5 2 2 1 CROSSREFS Row 1 of A249466. Sequence in context: A249001 A249466 A249002 * A309924 A120339 A319334 Adjacent sequences: A249464 A249465 A249466 * A249468 A249469 A249470 KEYWORD nonn AUTHOR R. H. Hardin, Oct 29 2014 STATUS approved

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Last modified September 10 20:50 EDT 2024. Contains 375794 sequences. (Running on oeis4.)