A249291 Number of length 1+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

14, 66, 204, 524, 1098, 2070, 3584, 5808, 8934, 13202, 18828, 26100, 35306, 46758, 60792, 77792, 98118, 122202, 150476, 183396, 221442, 265142, 315000, 371592, 435494, 507306, 587652, 677204, 776610, 886590, 1007864, 1141176, 1287294

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-5) + 2*a(n-6) - 3*a(n-7) +a(n- 8).

Empirical for n mod 6 = 0: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n

Empirical for n mod 6 = 1: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n + (7/3)

Empirical for n mod 6 = 2: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n + (8/3)

Empirical for n mod 6 = 3: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n - 3

Empirical for n mod 6 = 4: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n + (16/3)

Empirical for n mod 6 = 5: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n - (1/3).

Empirical g.f.: 2*x*(7 + 12*x + 17*x^2 + 29*x^3 + 7*x^5) / ((1 - x)^5*(1 + x)*(1 + x + x^2)). - Colin Barker, Nov 09 2018

Example

Some solutions for n=10:
  3  3  2  5  3  1  7  2  9  5  9  1  9  6  0  0
  3  7  0  9  5  7 10  0  8  9  2  5  5  7  1  5
  1  3  8 10  6  7  3  1  7  8  1  9  3  0  2  9
  1  1  4  6  0  3 10  9  0  2 10  8  4  4 10  1

Crossrefs

Row 1 of A249290.

Sequence in context: A213757 A249290 A336744 * A280401 A221703 A064096

Adjacent sequences: A249288 A249289 A249290 * A249292 A249293 A249294

Keyword

nonn

Author

R. H. Hardin, Oct 24 2014

Status

approved