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%I #5 Mar 31 2012 12:36:39
%S 0,20,0,92,80,0,248,520,212,0,520,1830,2232,594,0,940,4750,11008,9898,
%T 1928,0,1540,10250,36952,67852,50592,6780,0,2352,19530,98052,293464,
%U 473034,270848,23674,0,3408,34020,221984,955602,2591502,3397130,1432402
%N T(n,k)=Number of -k..k arrays x(0..n+2) of n+3 elements with zero sum and no two or three adjacent elements summing to zero
%C Table starts
%C .0.....20........92........248..........520...........940...........1540
%C .0.....80.......520.......1830.........4750.........10250..........19530
%C .0....212......2232......11008........36952.........98052.........221984
%C .0....594......9898......67852.......293464........955602........2567334
%C .0...1928.....50592.....473034......2591502......10217182.......32233938
%C .0...6780....270848....3397130.....23380862.....111101654......410475622
%C .0..23674...1432402...24220966....210222830....1206988576.....5230842688
%C .0..80750...7469120..171351382...1882624856...13090995142....66651385442
%C .0.271000..38883992.1214558880..16911040968..142480007436...852399648492
%C .0.909282.203526914.8651325238.152565274262.1556876199472.10942076565344
%H R. H. Hardin, <a href="/A200430/b200430.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical for rows:
%F T(1,k) = (16/3)*k^3 - 6*k^2 + (2/3)*k
%F T(2,k) = (115/12)*k^4 - (65/6)*k^3 + (65/12)*k^2 - (25/6)*k
%F T(3,k) = (88/5)*k^5 - (109/3)*k^4 + 44*k^3 - (107/3)*k^2 + (52/5)*k
%F T(4,k) = (5887/180)*k^6 - (5813/60)*k^5 + (6083/36)*k^4 - (2191/12)*k^3 + (9119/90)*k^2 - (353/15)*k
%F T(5,k) = (19328/315)*k^7 - (18373/90)*k^6 + (18602/45)*k^5 - (20887/36)*k^4 + (46687/90)*k^3 - (48359/180)*k^2 + (12499/210)*k
%F T(6,k) = (259723/2240)*k^8 - (2162653/5040)*k^7 + (1479629/1440)*k^6 - (642659/360)*k^5 + (6107509/2880)*k^4 - (1200571/720)*k^3 + (3930541/5040)*k^2 - (22719/140)*k
%F T(7,k) = (124952/567)*k^9 - (282778/315)*k^8 + (4520071/1890)*k^7 - (849277/180)*k^6 + (731309/108)*k^5 - (629357/90)*k^4 + (55560059/11340)*k^3 - (870757/420)*k^2 + (50299/126)*k
%e Some solutions for n=4 k=3
%e ..1....2...-2...-2....1....3....0....0....3....0...-2...-1...-2....3...-3....1
%e .-2...-3....1...-3....3....1....2....3....0....3....3...-3...-3....0...-3....3
%e ..3...-3...-3....0....2...-3....3....1...-2....2....1....2....2...-2....2....0
%e ..0...-2...-1....2...-1...-3....0....0...-3....0...-3....0....2....3....2...-2
%e .-1....3....2....2....0....0...-2....1....1....1...-2...-1....0....1....0....3
%e ..0....2....0....0...-2...-1....0...-3....0...-3....3....2....1...-3....3...-2
%e .-1....1....3....1...-3....3...-3...-2....1...-3....0....1....0...-2...-1...-3
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Nov 17 2011
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