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

Author

R. H. Hardin Nov 11 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 1 is A049450

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