A247535 Number of length 3+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

8, 61, 220, 561, 1124, 2009, 3220, 4901, 7016, 9737, 13000, 17025, 21688, 27245, 33572, 40929, 49140, 58553, 68924, 80613, 93400, 107641, 123056, 140113, 158440, 178509, 200012, 223393, 248260, 275209, 303748, 334453, 366920, 401689, 438264

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-2) + 2*a(n-3) + a(n-4) - 2*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) + 2*a(n-9) + a(n-10) - a(n-12).

Also as a cubic plus a linear quasipolynomial with period 12:

Empirical for n mod 12 = 0: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n + 1

Empirical for n mod 12 = 1: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (385/54)

Empirical for n mod 12 = 2: a(n) = (563/54)*n^3 - (127/18)*n^2 + (10/9)*n + (97/27)

Empirical for n mod 12 = 3: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (19/2)

Empirical for n mod 12 = 4: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n - (37/27)

Empirical for n mod 12 = 5: a(n) = (563/54)*n^3 - (127/18)*n^2 - (61/18)*n + (761/54)

Empirical for n mod 12 = 6: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n - 1

Empirical for n mod 12 = 7: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (385/54)

Empirical for n mod 12 = 8: a(n) = (563/54)*n^3 - (127/18)*n^2 + (10/9)*n + (151/27)

Empirical for n mod 12 = 9: a(n) = (563/54)*n^3 - (127/18)*n^2 - (5/2)*n + (19/2)

Empirical for n mod 12 = 10: a(n) = (563/54)*n^3 - (127/18)*n^2 + 2*n - (91/27)

Empirical for n mod 12 = 11: a(n) = (563/54)*n^3 - (127/18)*n^2 - (61/18)*n + (761/54).

Empirical g.f.: x*(8 + 61*x + 212*x^2 + 484*x^3 + 774*x^4 + 963*x^5 + 892*x^6 + 661*x^7 + 330*x^8 + 120*x^9 - x^11) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 07 2018

Example

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

Crossrefs

Row 3 of A247533.

Sequence in context: A242084 A007399 A071401 * A283852 A283410 A081907

Adjacent sequences: A247532 A247533 A247534 * A247536 A247537 A247538

Keyword

nonn

Author

R. H. Hardin, Sep 18 2014

Status

approved