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A200430
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
14
0, 20, 0, 92, 80, 0, 248, 520, 212, 0, 520, 1830, 2232, 594, 0, 940, 4750, 11008, 9898, 1928, 0, 1540, 10250, 36952, 67852, 50592, 6780, 0, 2352, 19530, 98052, 293464, 473034, 270848, 23674, 0, 3408, 34020, 221984, 955602, 2591502, 3397130, 1432402
OFFSET
1,2
COMMENTS
Table starts
.0.....20........92........248..........520...........940...........1540
.0.....80.......520.......1830.........4750.........10250..........19530
.0....212......2232......11008........36952.........98052.........221984
.0....594......9898......67852.......293464........955602........2567334
.0...1928.....50592.....473034......2591502......10217182.......32233938
.0...6780....270848....3397130.....23380862.....111101654......410475622
.0..23674...1432402...24220966....210222830....1206988576.....5230842688
.0..80750...7469120..171351382...1882624856...13090995142....66651385442
.0.271000..38883992.1214558880..16911040968..142480007436...852399648492
.0.909282.203526914.8651325238.152565274262.1556876199472.10942076565344
LINKS
FORMULA
Empirical for rows:
T(1,k) = (16/3)*k^3 - 6*k^2 + (2/3)*k
T(2,k) = (115/12)*k^4 - (65/6)*k^3 + (65/12)*k^2 - (25/6)*k
T(3,k) = (88/5)*k^5 - (109/3)*k^4 + 44*k^3 - (107/3)*k^2 + (52/5)*k
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
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
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
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
EXAMPLE
Some solutions for n=4 k=3
..1....2...-2...-2....1....3....0....0....3....0...-2...-1...-2....3...-3....1
.-2...-3....1...-3....3....1....2....3....0....3....3...-3...-3....0...-3....3
..3...-3...-3....0....2...-3....3....1...-2....2....1....2....2...-2....2....0
..0...-2...-1....2...-1...-3....0....0...-3....0...-3....0....2....3....2...-2
.-1....3....2....2....0....0...-2....1....1....1...-2...-1....0....1....0....3
..0....2....0....0...-2...-1....0...-3....0...-3....3....2....1...-3....3...-2
.-1....1....3....1...-3....3...-3...-2....1...-3....0....1....0...-2...-1...-3
CROSSREFS
Sequence in context: A324274 A070708 A370308 * A084029 A343329 A008426
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Nov 17 2011
STATUS
approved