%I #6 Dec 12 2014 20:23:25
%S 32,396,32,2292,702,32,9080,5316,1264,32,28020,27800,12612,2314,32,
%T 72972,104620,86736,30404,4308,32,167576,329742,397988,274204,74132,
%U 8150,32,349392,884032,1514488,1530604,874884,182084,15640,32,674520,2131356
%N T(n,k)=Number of length n+5 0..k arrays with no disjoint triples in any consecutive six terms having the same sum
%C Table starts
%C .32....396....2292......9080......28020.......72972.......167576........349392
%C .32....702....5316.....27800.....104620......329742.......884032.......2131356
%C .32...1264...12612.....86736.....397988.....1514488......4733944......13169096
%C .32...2314...30404....274204....1530604.....7023686.....25559480......81945184
%C .32...4308...74132....874884....5921416....32751572....138568024.....511733540
%C .32...8150..182084...2808970...22963328...153115250....752268668....3199929582
%C .32..15640..448956...9057366...89060732...716467630...4083208500...20012299980
%C .32..30620.1112546..29402376..346013066..3360812402..22177936206..125265598534
%C .32..60192.2766188..95651698.1346084716.15777745722.120522456308..784380367170
%C .32.118756.6890602.311754322.5240401580.74117488694.655151391416.4912998973440
%H R. H. Hardin, <a href="/A247995/b247995.txt">Table of n, a(n) for n = 1..468</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) +10*a(n-6) -20*a(n-7) -16*a(n-12) +32*a(n-13)
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8); also polynomial of degree 6 plus a degree 0 quasipolynomial with period 2
%F n=2: [order 18; also polynomial of degree 7 plus a cubic quasipolynomial with period 12]
%e Some solutions for n=3 k=4
%e ..2....4....4....4....1....4....3....3....3....2....2....1....2....1....2....2
%e ..1....3....4....4....4....3....0....4....4....0....0....4....4....3....3....0
%e ..1....1....1....0....2....0....0....3....2....0....4....4....4....3....0....3
%e ..1....3....1....1....4....0....4....2....0....2....1....4....1....4....2....0
%e ..1....0....1....2....1....3....0....2....0....2....3....0....2....0....4....3
%e ..1....2....3....0....4....1....2....3....0....4....3....1....4....4....4....3
%e ..3....0....1....2....1....4....1....1....4....1....0....0....4....4....0....4
%e ..1....3....1....2....1....3....0....0....0....2....0....0....1....4....3....3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Sep 28 2014