A248069 Number of length 1+5 0..n arrays with some disjoint triples in each consecutive six terms having the same sum.

32, 333, 1804, 6545, 18636, 44677, 94568, 182049, 325480, 548381, 880212, 1356913, 2021684, 2925525, 4128016, 5697857, 7713648, 10264429, 13450460, 17383761, 22188892, 28003493, 34979064, 43281505, 53091896, 64607037, 78040228, 93621809

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7).

Empirical for n mod 2 = 0: a(n) = (11/2)*n^5 - (5/2)*n^4 + (45/2)*n^3 + 10*n^2 - 12*n + 1.

Empirical for n mod 2 = 1: a(n) = (11/2)*n^5 - (5/2)*n^4 + (45/2)*n^3 + 10*n^2 - 12*n + (17/2).

Empirical g.f.: x*(32 + 173*x + 427*x^2 + 362*x^3 + 322*x^4 + 5*x^5 - x^6) / ((1 - x)^6*(1 + x)). - Colin Barker, Nov 08 2018

Example

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

Crossrefs

Row 1 of A248068.

Sequence in context: A223017 A293288 A248068 * A145402 A009797 A240293

Adjacent sequences: A248066 A248067 A248068 * A248070 A248071 A248072

Keyword

nonn

Author

R. H. Hardin, Sep 30 2014

Status

approved