A247534 Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

8, 45, 136, 317, 600, 1033, 1616, 2409, 3400, 4661, 6168, 8005, 10136, 12657, 15520, 18833, 22536, 26749, 31400, 36621, 42328, 48665, 55536, 63097, 71240, 80133, 89656, 99989, 111000, 122881, 135488, 149025, 163336, 178637, 194760, 211933, 229976

Offset

1,1

Links

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

Formula

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

Also as a cubic plus a linear quasipolynomial with period 2:

Empirical for n mod 2 = 0: a(n) = (9/2)*n^3 + (3/2)*n^2 + 1*n + 1

Empirical for n mod 2 = 1: a(n) = (9/2)*n^3 + (3/2)*n^2 - (1/2)*n + (5/2).

Empirical g.f.: x*(8 + 29*x + 38*x^2 + 32*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2). - Colin Barker, Nov 07 2018

Example

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

Crossrefs

Row 2 of A247533.

Sequence in context: A153828 A247834 A210378 * A100648 A128091 A119950

Adjacent sequences: A247531 A247532 A247533 * A247535 A247536 A247537

Keyword

nonn

Author

R. H. Hardin, Sep 18 2014

Status

approved