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.

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

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