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A200192 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

%I A200192 #7 Jul 22 2025 15:44:07
%S A200192 1,1,2,1,4,0,1,6,6,2,1,8,14,14,0,1,10,28,48,24,2,1,12,44,120,144,54,0,
%T A200192 1,14,66,242,506,482,104,2,1,16,90,426,1298,2240,1534,230,0,1,18,120,
%U A200192 688,2794,7266,9856,5148,464,2,1,20,152,1040,5300,18838,40632,44562,16826
%N A200192 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.
%C A200192 Table starts
%C A200192 .1....1.....1......1.......1........1.........1.........1..........1..........1
%C A200192 .2....4.....6......8......10.......12........14........16.........18.........20
%C A200192 .0....6....14.....28......44.......66........90.......120........152........190
%C A200192 .2...14....48....120.....242......426.......688......1040.......1494.......2066
%C A200192 .0...24...144....506....1298.....2794......5300......9220......14974......23094
%C A200192 .2...54...482...2240....7266....18838.....41938.....83600.....153278.....263198
%C A200192 .0..104..1534...9856...40632...127800....334278....765598....1585416....3034396
%C A200192 .2..230..5148..44562..231916...881008...2702398...7100700...16594066...35377058
%C A200192 .0..464.16826.199932.1320876..6081086..21910764..66127278..174522934..414666246
%C A200192 .2.1028.56918.914676.7630236.42452472.179391752.621239172.1850379990.4897547876
%H A200192 R. H. Hardin, <a href="/A200192/b200192.txt">Table of n, a(n) for n = 1..871</a>
%e A200192 Some solutions for n=6 k=5
%e A200192 .-4....0....5....2....4...-4....5....4....1....4....1...-3...-3...-1....4....0
%e A200192 ..3....3...-4....4...-3....2...-5...-2...-3...-3...-1....5....0....3...-3...-2
%e A200192 .-4...-4....1...-5....5...-2....4....1....3....3....3...-5...-3...-1....0....3
%e A200192 ..2....2...-4....1...-5....4...-5...-2...-1...-4...-4....5....5....1...-2...-2
%e A200192 ..0...-5....4...-5....4...-3....4....3....1....4....5...-2...-3...-2....2....4
%e A200192 ..3....4...-2....3...-5....3...-3...-4...-1...-4...-4....0....4....0...-1...-3
%Y A200192 Row 3 is A139596(n-1)
%K A200192 nonn,tabl
%O A200192 1,3
%A A200192 _R. H. Hardin_ Nov 14 2011