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A202962 T(n,k)=Number of arrays of n+2 integers in -k..k with sum zero and adjacent elements differing in absolute value.

%I A202962 #7 Jul 22 2025 16:53:56
%S A202962 2,6,4,20,28,2,36,108,82,0,62,268,414,200,6,90,544,1562,1936,524,12,
%T A202962 128,972,4048,9884,9872,1724,6,168,1576,9010,33736,66208,47732,5908,0,
%U A202962 218,2392,17296,90604,289536,447528,229714,18340,20,270,3456,30648,207184
%N A202962 T(n,k)=Number of arrays of n+2 integers in -k..k with sum zero and adjacent elements differing in absolute value.
%C A202962 Table starts
%C A202962 ..2......6.......20........36..........62...........90..........128
%C A202962 ..4.....28......108.......268.........544..........972.........1576
%C A202962 ..2.....82......414......1562........4048.........9010........17296
%C A202962 ..0....200.....1936......9884.......33736........90604.......207184
%C A202962 ..6....524.....9872.....66208......289536.......941086......2537024
%C A202962 .12...1724....47732....447528.....2475008......9824176.....31155004
%C A202962 ..6...5908...229714...3020170....21274708....102972822....384996502
%C A202962 ..0..18340..1134036..20430512...184258272...1085236504...4786979780
%C A202962 .20..53680..5624396.139027620..1602929218..11493823804..59791891464
%C A202962 .40.162080.27808428.950710524.13990833912.122199247152.749603860520
%H A202962 R. H. Hardin, <a href="/A202962/b202962.txt">Table of n, a(n) for n = 1..9784</a>
%e A202962 Some solutions for n=5 k=3
%e A202962 ..1....2....2....0...-1...-3....0....1....1....2....1....0...-3....1....2....2
%e A202962 .-3...-3....0...-3....0...-2....2...-3....0....3....3....1....1...-2....0...-3
%e A202962 ..0...-1...-1...-1...-1....0...-1...-1...-1....2...-1....2....3...-1...-1....0
%e A202962 .-1....0....3....0....2....2....0...-3...-2...-3....2...-3...-1...-3....0....1
%e A202962 ..2...-2...-2....3...-3....1...-3....1....3...-1...-3....2....2....2....1....2
%e A202962 ..3....1...-3....1....2....2...-1....2...-1...-3...-2...-3....0....1...-2....1
%e A202962 .-2....3....1....0....1....0....3....3....0....0....0....1...-2....2....0...-3
%Y A202962 Column 1 is A202069
%K A202962 nonn,tabl
%O A202962 1,1
%A A202962 _R. H. Hardin_ Dec 26 2011