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 A245868 Number of length n+2 0..7 arrays with some pair in every consecutive three terms totalling exactly 7. 1

%I #11 May 13 2020 18:59:53

%S 168,712,2368,8840,31176,113024,404264,1455496,5223552,18775816,

%T 67437448,242306240,870461352,3127322696,11235107264,40363689352,

%U 145010699592,520968428032,1871637364264,6724074597128,24157004951808,86786820122120

%N Number of length n+2 0..7 arrays with some pair in every consecutive three terms totalling exactly 7.

%H R. H. Hardin, <a href="/A245868/b245868.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A245868/a245868.pdf">Maple-assisted derivation of recurrence</a>

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

%F Empirical g.f.: 8*x*(21 + 47*x - 8*x^2) / (1 - 2*x - 6*x^2 + x^3). - _Colin Barker_, Nov 04 2018

%F Empirical recurrence verified: see link. - _Robert Israel_, May 13 2020

%e Some solutions for n=6:

%e ..4....6....7....0....7....3....6....4....0....2....6....1....6....5....0....2

%e ..2....4....6....0....2....6....3....5....7....6....0....7....6....6....7....5

%e ..3....3....1....7....0....1....4....2....6....1....1....0....1....2....6....6

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

%e ..2....1....3....0....2....5....7....5....0....6....7....6....6....6....7....7

%e ..4....6....4....3....4....2....2....2....7....1....0....6....7....7....2....6

%e ..5....3....3....4....3....5....5....0....5....1....7....1....0....0....5....1

%e ..2....4....2....3....2....4....6....5....2....6....0....2....2....6....3....7

%Y Column 7 of A245869.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 04 2014

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Last modified September 30 02:05 EDT 2023. Contains 365781 sequences. (Running on oeis4.)