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A189498 T(n,k)=Number of arrangements of n+1 nonzero numbers x(i) in -k..k with the sum of floor(x(i)/x(i+1)) equal to zero.

%I A189498 #7 Jul 22 2025 11:47:17
%S A189498 0,2,4,6,12,0,12,38,42,12,20,78,152,136,0,30,148,462,928,550,40,42,
%T A189498 240,1088,3388,4920,1892,0,56,380,2128,9394,24806,27508,7384,140,72,
%U A189498 554,3850,22088,85480,182634,152358,26816,0,90,788,6474,45892,238836,787412
%N A189498 T(n,k)=Number of arrangements of n+1 nonzero numbers x(i) in -k..k with the sum of floor(x(i)/x(i+1)) equal to zero.
%C A189498 Table starts
%C A189498 ...0......2........6........12.........20..........30...........42...........56
%C A189498 ...4.....12.......38........78........148.........240..........380..........554
%C A189498 ...0.....42......152.......462.......1088........2128.........3850.........6474
%C A189498 ..12....136......928......3388.......9394.......22088........45892........86416
%C A189498 ...0....550.....4920.....24806......85480......238836.......567774......1218778
%C A189498 ..40...1892....27508....182634.....787412.....2642358......7269852.....17692662
%C A189498 ...0...7384...152358...1350418....7250142....29261538.....93830584....260746932
%C A189498 .140..26816...852940..10077438...67449574...326423068...1218634086...3870426602
%C A189498 ...0.103288..4796962..75593372..630466648..3664621084..15936391068..57837221756
%C A189498 .504.386928.27117826.569975518.5926141678.41363200538.209537582772.869215927390
%H A189498 R. H. Hardin, <a href="/A189498/b189498.txt">Table of n, a(n) for n = 1..797</a>
%e A189498 Some solutions for n=7 k=5
%e A189498 .-5...-5...-5...-5...-5...-4...-5...-5...-5...-4...-5...-5...-5...-5...-5...-5
%e A189498 .-5...-5...-5...-5...-5...-5...-5...-5...-5...-5...-5...-5...-5...-5...-5...-5
%e A189498 ..3...-4....5....2....3...-4....4...-4...-3...-5....5....5....1....1....3....3
%e A189498 .-4....3...-4...-3....2...-3....3....5....1...-3...-4....2....4....2....1....2
%e A189498 .-2....2...-1...-4...-1...-5....1....4....1...-4...-2...-5....2....2...-1....5
%e A189498 ..4....5...-3....4...-5...-2...-2....3....2...-5....2....3...-5...-4...-5...-5
%e A189498 ..3...-2....2....2...-4....5...-4...-1....2....3....3....5...-5...-1....3...-2
%e A189498 ..5...-1....5....1...-4...-2....3...-4...-4....4....3....5...-2...-4....3....2
%Y A189498 Column 1 is A028329(n/2) for even n
%Y A189498 Row 1 is A002378(n-1)
%K A189498 nonn,tabl
%O A189498 1,2
%A A189498 _R. H. Hardin_ Apr 23 2011