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T(n,k)=Number of arrays of n+2 integers in -k..k with sum zero and the sum of every adjacent pair being odd
12

%I #5 Mar 31 2012 12:36:46

%S 2,4,4,10,20,2,14,56,26,0,24,120,78,0,6,30,220,264,0,96,12,44,364,504,

%T 0,1014,524,6,52,560,1128,0,3752,5832,726,0,70,816,1786,0,15010,34632,

%U 8412,0,20,80,1140,3262,0,35604,142692,80812,0,2760,40,102,1540,4660,0,95342

%N T(n,k)=Number of arrays of n+2 integers in -k..k with sum zero and the sum of every adjacent pair being odd

%C Table starts

%C ..2.....4.....10.......14........24........30.........44..........52

%C ..4....20.....56......120.......220.......364........560.........816

%C ..2....26.....78......264.......504......1128.......1786........3262

%C ..0.....0......0........0.........0.........0..........0...........0

%C ..6....96...1014.....3752.....15010.....35604......95342......181834

%C .12...524...5832....34632....142692....462436....1264272.....3044496

%C ..6...726...8412....80812....340660...1516410....4213042....12861252

%C ..0.....0......0........0.........0.........0..........0...........0

%C .20..2760.118560..1201220..10924220..50331332..241384794...755963886

%C .40.15560.691352.11395632.105606040.670671976.3259289000.12973320840

%H R. H. Hardin, <a href="/A202076/b202076.txt">Table of n, a(n) for n = 1..9999</a>

%e Some solutions for n=3 k=3

%e ..0....0....0....2....2....0....2....2....0....0....0...-2....2....0...-2...-2

%e ..1...-1....3....1...-1....1....1...-1....1...-1...-1....3...-3...-3....3....3

%e .-2...-2...-2...-2....0....2....0....0....0....2....0...-2....2....2...-2....0

%e ..1....1...-3...-3....1...-3...-1...-3...-3...-1....3....3...-3...-1...-1...-3

%e ..0....2....2....2...-2....0...-2....2....2....0...-2...-2....2....2....2....2

%Y Row 1 is A152749

%Y Row 2 is A002492

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Dec 10 2011