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

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

R. H. Hardin, Table of n, a(n) for n = 1..544

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

Adjacent sequences: A200427 A200428 A200429 * A200431 A200432 A200433

Keyword

nonn,tabl

Author

R. H. Hardin Nov 17 2011

Status

approved