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A247996 Number of length 1+5 0..n arrays with no disjoint triples in any consecutive six terms having the same sum. 1
32, 396, 2292, 9080, 28020, 72972, 167576, 349392, 674520, 1223180, 2105772, 3469896, 5507852, 8465100, 12649200, 18439712, 26298576, 36781452, 50549540, 68382360, 91191012, 120032396, 156123912, 200859120, 255823880, 322813452 (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) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8).

Empirical for n mod 2 = 0: a(n) = n^6 + (1/2)*n^5 + (35/2)*n^4 - (5/2)*n^3 + 5*n^2 + 18*n

Empirical for n mod 2 = 1: a(n) = n^6 + (1/2)*n^5 + (35/2)*n^4 - (5/2)*n^3 + 5*n^2 + 18*n - (15/2).

Conjectures from Colin Barker, Nov 07 2018: (Start)

G.f.: 4*x*(8 + 51*x + 91*x^2 + 106*x^3 + 21*x^4 + 83*x^5) / ((1 - x)^7*(1 + x)).

a(n) = (2*n^6 + n^5 + 35*n^4 - 5*n^3 + 10*n^2 + 36*n) / 2 for n even.

a(n) = (2*n^6 + n^5 + 35*n^4 - 5*n^3 + 10*n^2 + 36*n - 15) / 2 for n odd.

(End)

EXAMPLE

Some solutions for n=6:

  4  3  5  2  0  5  4  4  0  1  6  1  5  4  4  2

  4  1  5  0  3  4  0  1  0  6  4  6  4  4  1  0

  2  0  3  4  5  5  3  1  5  3  5  5  1  2  2  2

  6  1  3  1  2  0  4  1  2  4  5  1  5  2  5  0

  3  2  2  5  2  2  2  1  1  0  5  5  3  5  3  2

  0  6  5  3  5  1  2  0  0  5  6  2  3  6  2  5

CROSSREFS

Row 1 of A247995.

Sequence in context: A128798 A086942 A247995 * A068548 A195191 A275232

Adjacent sequences:  A247993 A247994 A247995 * A247997 A247998 A247999

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 28 2014

STATUS

approved

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Last modified January 18 21:06 EST 2021. Contains 340262 sequences. (Running on oeis4.)