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A247535 Number of length 3+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)