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 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 17
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)