A242235 Number of length n+4+1 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+2 elements, and new values 0..4 introduced in order.

15, 35, 71, 139, 271, 531, 1047, 2059, 4047, 7955, 15639, 30747, 60447, 118835, 233623, 459291, 902943, 1775139, 3489831, 6860827, 13488031, 26516771, 52130599, 102486059, 201482287, 396103747, 778719463, 1530922155, 3009713711

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5).

Conjecture: a(n) = 16*A145113(n-1) + A004767(n-2), n > 1. - R. J. Mathar, Aug 16 2017

Empirical g.f.: x*(15 + 20*x + 21*x^2 + 18*x^3 + 11*x^4) / (1 - x - x^2 - x^3 - x^4 - x^5). - Colin Barker, Oct 31 2018

Example

Some solutions for n=5:
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  0  1  1  1  1  1  1  1  1  0  1  1  0  1  1  1
  1  2  2  2  2  0  2  0  0  1  2  2  1  2  2  2
  2  3  0  1  3  2  3  2  2  2  2  3  2  0  3  0
  3  2  3  3  4  3  0  3  3  3  3  4  3  3  0  3
  4  4  4  4  1  4  4  4  4  4  4  1  4  4  4  4
  1  0  1  0  0  1  1  0  0  2  0  0  0  0  1  2
  0  1  2  3  2  2  2  1  1  0  1  2  1  1  2  1
  4  3  3  2  2  0  3  1  3  1  2  4  2  2  3  0
  2  0  0  1  3  1  4  2  2  0  1  3  2  2  0  1

Crossrefs

Cf. A004767, A145113, A242239.

Column 4 of A242239.

Sequence in context: A160497 A098271 A234542 * A082663 A368231 A109068

Adjacent sequences: A242232 A242233 A242234 * A242236 A242237 A242238

Keyword

nonn

Author

R. H. Hardin, May 08 2014

Status

approved