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A245873 Number of length 4+2 0..n arrays with some pair in every consecutive three terms totalling exactly n. 1

%I

%S 26,239,676,1629,3102,5515,8840,13625,19810,28071,38316,51349,67046,

%T 86339,109072,136305,167850,204895,247220,296141,351406,414459,485016,

%U 564649,653042,751895,860860,981765,1114230,1260211,1419296,1593569

%N Number of length 4+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

%H R. H. Hardin, <a href="/A245873/b245873.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7).

%F Conjectures from _Colin Barker_, Nov 04 2018: (Start)

%F G.f.: x*(26 + 161*x - 15*x^2 - 30*x^3 - 44*x^4 - 3*x^5 + x^6) / ((1 - x)^5*(1 + x)^2).

%F a(n) = 1 + 7*n + 20*n^2 + 16*n^3 + n^4 for n even.

%F a(n) = -8 - 3*n + 20*n^2 + 16*n^3 + n^4 for n odd.

%F (End)

%e Some solutions for n=10:

%e 0 6 8 3 8 4 7 8 7 1 8 10 4 3 7 1

%e 10 5 6 10 6 2 3 9 4 0 1 2 5 3 4 0

%e 4 4 4 0 4 6 3 1 3 10 9 8 5 7 6 10

%e 6 5 10 7 4 8 7 1 7 1 3 7 3 3 10 0

%e 1 5 0 10 6 2 6 9 8 0 7 3 7 1 0 4

%e 4 8 7 0 0 0 4 7 3 10 7 4 9 7 9 10

%Y Row 4 of A245869.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 04 2014

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)