login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A247996
Number of length 1+5 0..n arrays with no disjoint triples in any consecutive six terms having the same sum.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 28 2014
STATUS
approved