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A247729 Number of length 3+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum 1
8, 172, 1248, 5796, 19744, 55372, 133780, 290004, 576064, 1068584, 1871996, 3129068, 5023940, 7795872, 11741676, 17233232, 24718860, 34744832, 47955536, 65119328, 87126876, 115022012, 149997832, 193432664, 246883888, 312129332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A247726

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -2*a(n-4) -2*a(n-5) +5*a(n-6) +2*a(n-7) -2*a(n-9) -5*a(n-10) +2*a(n-11) +2*a(n-12) +2*a(n-13) -a(n-14) -2*a(n-15) +a(n-16)

Empirical for n mod 12 = 0: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (62/9)*n^2 - (5/3)*n

Empirical for n mod 12 = 1: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (35/9)*n^2 + (23/6)*n - (223/54)

Empirical for n mod 12 = 2: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (62/9)*n^2 - (7/9)*n - (70/27)

Empirical for n mod 12 = 3: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (35/9)*n^2 + (23/6)*n - (13/2)

Empirical for n mod 12 = 4: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (62/9)*n^2 - (5/3)*n + (64/27)

Empirical for n mod 12 = 5: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (35/9)*n^2 + (85/18)*n - (599/54)

Empirical for n mod 12 = 6: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (62/9)*n^2 - (5/3)*n + 2

Empirical for n mod 12 = 7: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (35/9)*n^2 + (23/6)*n - (223/54)

Empirical for n mod 12 = 8: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (62/9)*n^2 - (7/9)*n - (124/27)

Empirical for n mod 12 = 9: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (35/9)*n^2 + (23/6)*n - (13/2)

Empirical for n mod 12 = 10: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (62/9)*n^2 - (5/3)*n + (118/27)

Empirical for n mod 12 = 11: a(n) = 1*n^6 + (43/6)*n^4 - (203/54)*n^3 + (35/9)*n^2 + (85/18)*n - (599/54)

Empirical g.f.: -4*x* (2 +39*x +224*x^2 +786*x^3 +1816*x^4 +3236*x^5 +4421*x^6 +4943*x^7 +4379*x^8 +3196*x^9 +1787*x^10 +795*x^11 +235*x^12 +61*x^13) / ( (x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^7 ). - R. J. Mathar, Sep 23 2014

EXAMPLE

Some solutions for n=6

..3....0....0....6....6....6....5....6....2....2....3....2....6....5....5....2

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

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

..0....6....5....0....0....0....5....6....5....4....0....2....1....2....1....4

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

..2....1....5....6....0....6....6....0....4....1....6....5....5....6....5....6

CROSSREFS

Sequence in context: A317566 A301444 A333036 * A333460 A221060 A303285

Adjacent sequences:  A247726 A247727 A247728 * A247730 A247731 A247732

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 23 2014

STATUS

approved

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Last modified June 30 05:22 EDT 2022. Contains 354913 sequences. (Running on oeis4.)