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%I #8 Dec 18 2022 07:08:23
%S 2,2,3,2,11,4,2,17,20,5,2,25,61,57,6,2,36,104,159,88,7,2,47,186,411,
%T 365,180,8,2,62,275,800,968,847,254,9,2,78,431,1415,2560,2689,1488,
%U 439,10,2,94,585,2394,4932,7102,5573,2751,587,11,2,116,848,3848,9546,17203,17441
%N T(n,k)=Number of nondecreasing -k..k vectors of length n whose dot product with some lexicographically greater or equal nondecreasing -k..k vector equals n
%H R. H. Hardin, <a href="/A226422/b226422.txt">Table of n, a(n) for n = 1..160</a>
%e Table starts
%e ..2...2....2.....2......2......2.......2.......2.......2.......2.......2
%e ..3..11...17....25.....36.....47......62......78......94.....116.....142
%e ..4..20...61...104....186....275.....431.....585.....848....1080....1470
%e ..5..57..159...411....800...1415....2394....3848....5764....8484...12067
%e ..6..88..365...968...2560...4932....9546...16367...27678...43394...67854
%e ..7.180..847..2689...7102..17203...35451...67982..123055..211156..347133
%e ..8.254.1488..5573..17441..44256..108478..224471..443879..815019.1452101
%e ..9.439.2751.12301..41336.118669..302135..711442.1500739.2984761
%e .10.587.4739.22398..87716.275619..777184.1935009.4555068
%e .11.905.7551.41891.180915.628149.1900407.5151925
%e Some solutions for n=3 k=4
%e .-3...-1...-3...-1...-3...-4...-3...-2....0...-2...-4...-4...-4...-2...-1...-4
%e .-1...-1...-2...-1...-3....1....0...-2....0....3...-1...-1....1....2....1...-3
%e ..2....4...-2....1...-1....3....4....1....1....3....3....0....1....3....1...-1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jun 06 2013