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T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having four times the sum of any three elements equal to three times the sum of the remaining four
15

%I #4 Oct 23 2014 08:05:49

%S 126,1792,250,14126,4586,496,66948,49730,11874,984,240870,290032,

%T 175616,30876,1952,708106,1249890,1257084,620648,80354,3872,1809164,

%U 4264120,6487112,5448778,2194096,208876,7680,4132884,12523980,25682744,33673760

%N T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having four times the sum of any three elements equal to three times the sum of the remaining four

%C Table starts

%C ......126.......1792.........14126..........66948..........240870

%C ......250.......4586.........49730.........290032.........1249890

%C ......496......11874........175616........1257084.........6487112

%C ......984......30876........620648........5448778........33673760

%C .....1952......80354.......2194096.......23617364.......174811880

%C .....3872.....208876.......7758744......102366154.......907556600

%C .....7680.....541624......27446576......443680650......4711821902

%C ....15234....1400008......97142002.....1922960684.....24462953912

%C ....30218....3618986.....343823110.....8334332160....127008089170

%C ....59940....9363890....1217189036....36123881064....659412923000

%C ...118896...24245852....4309583172...156575247076...3423615122520

%H R. H. Hardin, <a href="/A249197/b249197.txt">Table of n, a(n) for n = 1..174</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6)

%e Some solutions for n=3 k=4

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....1....1....1....0....0....1....1....1....1....1....1....1....1....1....0

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 23 2014