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

Author

R. H. Hardin, Sep 18 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 2 of A247533.

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