A199832 T(n,k)=Number of -k..k arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero

2, 10, 4, 24, 40, 4, 44, 140, 114, 10, 70, 336, 646, 426, 22, 102, 660, 2146, 3556, 1650, 34, 140, 1144, 5390, 15708, 20240, 6126, 66, 184, 1820, 11384, 49302, 118280, 113884, 23206, 138, 234, 2720, 21364, 124982, 462234, 888420, 645780, 88636, 250, 290, 3876

Offset

1,1

Comments

Table starts

...2......10........24.........44..........70..........102...........140

...4......40.......140........336.........660.........1144..........1820

...4.....114.......646.......2146........5390........11384.........21364

..10.....426......3556......15708.......49302.......124982........273728

..22....1650.....20240.....118280......462234......1402934.......3579520

..34....6126....113884.....888420.....4340094.....15805218......47040968

..66...23206....645780....6715618....41008804....179213048.....622300326

.138...88636...3685550...51077518...389832124...2044221894....8281149188

.250..337866..21117750..390278378..3723199342..23427591518..110718596524

.472.1295566.121503530.2993722414.35697026718.269528370904.1486040082748

Links

R. H. Hardin, Table of n, a(n) for n = 1..788

Formula

Empirical for rows:

T(1,k) = 3*k^2 - k

T(2,k) = (16/3)*k^3 - (4/3)*k

T(3,k) = (115/12)*k^4 - (29/6)*k^3 + (5/12)*k^2 - (7/6)*k

T(4,k) = (88/5)*k^5 - (28/3)*k^4 + (2/3)*k^3 + (7/3)*k^2 - (19/15)*k

T(5,k) = (5887/180)*k^6 - (1013/60)*k^5 + (245/36)*k^4 - (35/12)*k^3 + (157/45)*k^2 - (6/5)*k

T(6,k) = (19328/315)*k^7 - (1424/45)*k^6 + (704/45)*k^5 - (112/9)*k^4 - (124/45)*k^3 + (229/45)*k^2 - (131/105)*k

T(7,k) = (259723/2240)*k^8 - (299869/5040)*k^7 + (39757/1440)*k^6 - (8303/360)*k^5 + (31829/2880)*k^4 - (8083/720)*k^3 + (32213/5040)*k^2 - (509/420)*k

T(8,k) = (124952/567)*k^9 - (35524/315)*k^8 + (50588/945)*k^7 - (2494/45)*k^6 + (13739/270)*k^5 - (1927/180)*k^4 - (41254/2835)*k^3 + (3319/420)*k^2 - (781/630)*k

Example

Some solutions for n=4 k=3
..3....2...-2...-3...-3....3...-1...-1....0...-1....3...-1....2...-3....1....3
..3....2....0....0....1...-2....0....2....2....2....3....0...-1...-1....3....1
.-2....0....1....1....2...-2....1....2....1....0....0....1...-3....2....2...-2
.-2...-1...-2....0....2....0...-3....2....1...-2...-2...-2...-1...-1...-3...-3
..1...-1....0....3....1....3....1...-3...-2...-1...-1....0....3....2...-1....2
.-3...-2....3...-1...-3...-2....2...-2...-2....2...-3....2....0....1...-2...-1

Crossrefs

Row 1 is A049450

Sequence in context: A189881 A189872 A319407 * A189878 A189869 A054790

Adjacent sequences: A199829 A199830 A199831 * A199833 A199834 A199835

Keyword

nonn,tabl

Author

R. H. Hardin Nov 11 2011

Status

approved