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%I #6 Dec 12 2014 20:24:04
%S 32,333,32,1804,513,32,6545,3364,793,32,18636,15125,6364,1221,32,
%T 44677,48316,35529,12124,1861,32,94568,131677,128556,83925,23164,2793,
%U 32,182049,299968,398737,345760,198333,44284,4113,32,325480,625269,983784
%N T(n,k)=Number of length n+5 0..k arrays with some disjoint triples in each consecutive six terms having the same sum
%C Table starts
%C .32...333...1804.....6545.....18636......44677......94568......182049
%C .32...513...3364....15125.....48316.....131677.....299968......625269
%C .32...793...6364....35529....128556.....398737.....983784.....2223873
%C .32..1221..12124....83925....345760....1220617....3273988.....8029409
%C .32..1861..23164...198333....933004....3747537...10950616....29138097
%C .32..2793..44284...467723...2517256...11500157...36646756...105799459
%C .32..4113..84604..1099415...6782344...35238445..122502768...383781973
%C .32..6753.161824..2676011..18295612..109996209..409950004..1407188901
%C .32.10945.309724..6485603..49388668..342828243.1372989004..5155470523
%C .32.17457.592924.15656957.133375284.1066829297.4600574912.18875673047
%H R. H. Hardin, <a href="/A248068/b248068.txt">Table of n, a(n) for n = 1..565</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +20*a(n-6) -20*a(n-7) -64*a(n-12) +64*a(n-13)
%F k=3: [order 16]
%F Empirical for row n:
%F n=1: a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7); also a degree 5 polynomial plus a quasipolynomial of degree zero with period 2
%F n=2: [order 16; also a degree 5 polynomial plus a cubic quasipolynomial with period 12]
%e Some solutions for n=4 k=4
%e ..2....2....0....3....2....3....1....3....2....4....0....2....3....0....0....1
%e ..4....2....1....0....4....3....1....3....0....2....3....4....1....2....4....3
%e ..2....3....1....0....1....2....4....3....3....2....1....1....2....2....2....0
%e ..2....1....3....3....3....4....2....3....4....3....2....3....3....2....0....2
%e ..3....3....3....4....3....2....2....1....1....2....4....4....4....3....1....4
%e ..3....1....2....4....1....2....2....1....0....3....0....2....1....3....1....2
%e ..0....0....0....3....2....1....1....3....2....2....4....2....1....2....0....3
%e ..0....4....1....2....4....1....3....3....0....0....1....4....1....0....0....1
%e ..2....3....1....4....1....4....4....3....1....0....3....1....2....4....0....4
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Sep 30 2014
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