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A200553 T(n,k)=Number of -k..k arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.

%I A200553 #7 Jul 22 2025 15:52:17
%S A200553 4,14,14,30,76,26,52,200,280,72,80,446,1184,1240,142,114,836,3396,
%T A200553 7254,4978,362,154,1368,7778,26850,43698,21626,778,200,2134,15476,
%U A200553 75792,211374,266812,91058,1938,252,3140,27806,178834,737460,1689732,1639804
%N A200553 T(n,k)=Number of -k..k arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences.
%C A200553 Table starts
%C A200553 .....4......14........30.........52..........80..........114...........154
%C A200553 ....14......76.......200........446.........836.........1368..........2134
%C A200553 ....26.....280......1184.......3396........7778........15476.........27806
%C A200553 ....72....1240......7254......26850.......75792.......178834........372150
%C A200553 ...142....4978.....43698.....211374......737460......2076774.......5012084
%C A200553 ...362...21626....266812....1689732.....7286542.....24378976......68263780
%C A200553 ...778...91058...1639804...13587804....72366820....288237528.....936121220
%C A200553 ..1938..393660..10152636..109957140...723237026...3427837106...12911643944
%C A200553 ..4366.1686980..63132188..893510530..7258296910..40950125796..178893425570
%C A200553 .10628.7309386.394016210.7288331916.73127883596.491063998130.2488110363432
%H A200553 R. H. Hardin, <a href="/A200553/b200553.txt">Table of n, a(n) for n = 1..715</a>
%e A200553 Some solutions for n=4 k=3
%e A200553 ..1....1...-1....1...-1...-3...-1...-1....2....3....3...-3...-2....1....0...-3
%e A200553 ..1...-1...-3...-2....1...-3...-3....1...-3....2...-2....2....1...-1....0....3
%e A200553 .-1...-2....3....3....0....0....2....2....1...-3....0....2....1....0....2....2
%e A200553 ..0....2...-3...-1....0....0....1....2...-2...-3...-3...-2....2...-2...-3...-2
%e A200553 .-3...-3....1...-3...-2....3....2...-3....3....0...-1...-1...-3....1....1....0
%e A200553 ..2....3....3....2....2....3...-1...-1...-1....1....3....2....1....1....0....0
%Y A200553 Row 1 is A049451
%K A200553 nonn,tabl
%O A200553 1,1
%A A200553 _R. H. Hardin_ Nov 19 2011