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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

%I

%S 8,172,1248,5796,19744,55372,133780,290004,576064,1068584,1871996,

%T 3129068,5023940,7795872,11741676,17233232,24718860,34744832,47955536,

%U 65119328,87126876,115022012,149997832,193432664,246883888,312129332

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

%C Row 3 of A247726

%H R. H. Hardin, <a href="/A247729/b247729.txt">Table of n, a(n) for n = 1..210</a>

%F 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)

%F 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

%F 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)

%F 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)

%F 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)

%F 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)

%F 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)

%F 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

%F 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)

%F 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)

%F 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)

%F 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)

%F 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)

%F 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

%e Some solutions for n=6

%e ..3....0....0....6....6....6....5....6....2....2....3....2....6....5....5....2

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

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

%e ..0....6....5....0....0....0....5....6....5....4....0....2....1....2....1....4

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

%e ..2....1....5....6....0....6....6....0....4....1....6....5....5....6....5....6

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 23 2014

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Last modified August 17 10:27 EDT 2022. Contains 356187 sequences. (Running on oeis4.)