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A183913 Number of nondecreasing arrangements of n numbers in -5..5 with sum zero.

%I A183913 #8 Jul 22 2025 09:17:55
%S A183913 1,6,18,55,141,338,734,1514,2934,5448,9686,16660,27718,44916,70922,
%T A183913 109583,165821,246448,360002,517971,734517,1028172,1421530,1943488,
%U A183913 2628824,3521260,4672836,6147894,8022362,10388788,13355414,17052653
%N A183913 Number of nondecreasing arrangements of n numbers in -5..5 with sum zero.
%C A183913 Column 5 of A183917
%H A183913 R. H. Hardin, <a href="/A183913/b183913.txt">Table of n, a(n) for n = 1..200</a>
%F A183913 Empirical: a(n)=a(n-1)+2*a(n-2)-a(n-3)-a(n-4)-a(n-5)+a(n-9)-a(n-10)+3*a(n-12)+a(n-13)-a(n-14)-a(n-16)-2*a(n-17)-a(n-18)-a(n-20)+a(n-22)+2*a(n-23)+2*a(n-24)+a(n-25)-a(n-27)-a(n-29)-2*a(n-30)-a(n-31)-a(n-33)+a(n-34)+3*a(n-35)-a(n-37)+a(n-38)-a(n-42)-a(n-43)-a(n-44)+2*a(n-45)+a(n-46)-a(n-47)
%e A183913 Some solutions for n=4
%e A183913 .-5...-4...-4...-5...-4...-4...-3...-4...-4...-2...-3...-5...-3...-1...-3...-3
%e A183913 .-1...-1...-2....0...-4....0...-3...-2....1...-1...-1...-2....0....0...-2...-1
%e A183913 ..2....1....1....0....3....1....1....2....1...-1...-1....2....1....0....0....1
%e A183913 ..4....4....5....5....5....3....5....4....2....4....5....5....2....1....5....3
%K A183913 nonn
%O A183913 1,2
%A A183913 _R. H. Hardin_ Jan 07 2011