A249285 Number of length n+3 0..3 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

204, 660, 2144, 6960, 22572, 73204, 237480, 770416, 2499164, 8107012, 26298608, 85311248, 276744204, 897739412, 2912207432, 9447011744, 30645489228, 99411957620, 322485877472, 1046123080816, 3393554802188, 11008469603188

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + 4*a(n-3) + 8*a(n-4) + 4*a(n-5) - 8*a(n-6) - 2*a(n-7) + 3*a(n-8).

Empirical g.f.: 4*x*(51 + 63*x + 104*x^2 + 134*x^3 + 23*x^4 - 133*x^5 - 18*x^6 + 48*x^7) / (1 - 2*x - 2*x^2 - 4*x^3 - 8*x^4 - 4*x^5 + 8*x^6 + 2*x^7 - 3*x^8). - Colin Barker, Nov 09 2018

Example

Some solutions for n=6:
  3  0  3  2  1  1  3  0  0  0  3  3  1  2  0  2
  3  1  3  2  0  1  1  0  1  2  1  3  0  3  2  2
  1  1  2  1  3  1  3  2  0  2  0  1  1  2  2  1
  2  1  3  1  3  0  1  0  2  0  1  1  1  2  0  0
  0  0  2  3  1  0  3  2  3  3  3  2  3  0  2  0
  2  3  0  3  1  1  0  2  0  1  1  2  0  0  0  1
  2  3  1  3  3  0  3  0  1  3  0  0  2  2  2  1
  3  0  3  1  3  1  3  3  1  1  2  1  0  3  1  3
  3  1  1  1  2  0  3  2  0  2  0  0  0  2  2  0

Crossrefs

Column 3 of A249290.

Sequence in context: A163393 A245468 A154518 * A292346 A338153 A234796

Adjacent sequences: A249282 A249283 A249284 * A249286 A249287 A249288

Keyword

nonn

Author

R. H. Hardin, Oct 24 2014

Status

approved