A247729 Number of length 3+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum

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

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