A247996 Number of length 1+5 0..n arrays with no disjoint triples in any consecutive six terms having the same sum.

32, 396, 2292, 9080, 28020, 72972, 167576, 349392, 674520, 1223180, 2105772, 3469896, 5507852, 8465100, 12649200, 18439712, 26298576, 36781452, 50549540, 68382360, 91191012, 120032396, 156123912, 200859120, 255823880, 322813452

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8).

Empirical for n mod 2 = 0: a(n) = n^6 + (1/2)*n^5 + (35/2)*n^4 - (5/2)*n^3 + 5*n^2 + 18*n

Empirical for n mod 2 = 1: a(n) = n^6 + (1/2)*n^5 + (35/2)*n^4 - (5/2)*n^3 + 5*n^2 + 18*n - (15/2).

Conjectures from Colin Barker, Nov 07 2018: (Start)

G.f.: 4*x*(8 + 51*x + 91*x^2 + 106*x^3 + 21*x^4 + 83*x^5) / ((1 - x)^7*(1 + x)).

a(n) = (2*n^6 + n^5 + 35*n^4 - 5*n^3 + 10*n^2 + 36*n) / 2 for n even.

a(n) = (2*n^6 + n^5 + 35*n^4 - 5*n^3 + 10*n^2 + 36*n - 15) / 2 for n odd.

(End)

Example

Some solutions for n=6:
  4  3  5  2  0  5  4  4  0  1  6  1  5  4  4  2
  4  1  5  0  3  4  0  1  0  6  4  6  4  4  1  0
  2  0  3  4  5  5  3  1  5  3  5  5  1  2  2  2
  6  1  3  1  2  0  4  1  2  4  5  1  5  2  5  0
  3  2  2  5  2  2  2  1  1  0  5  5  3  5  3  2
  0  6  5  3  5  1  2  0  0  5  6  2  3  6  2  5

Crossrefs

Row 1 of A247995.

Sequence in context: A128798 A086942 A247995 * A068548 A195191 A275232

Adjacent sequences: A247993 A247994 A247995 * A247997 A247998 A247999

Keyword

nonn

Author

R. H. Hardin, Sep 28 2014

Status

approved