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A188183 Number of strictly increasing arrangements of 5 numbers in -(n+3)..(n+3) with sum zero.

%I A188183 #9 Jul 22 2025 11:01:53
%S A188183 12,32,73,141,252,414,649,967,1394,1944,2649,3523,4604,5910,7483,9343,
%T A188183 11538,14090,17053,20451,24342,28754,33751,39361,45654,52662,60459,
%U A188183 69079,78602,89064,100551,113101,126804,141702,157891,175413,194370,214808
%N A188183 Number of strictly increasing arrangements of 5 numbers in -(n+3)..(n+3) with sum zero.
%C A188183 Row 5 of A188181
%H A188183 R. H. Hardin, <a href="/A188183/b188183.txt">Table of n, a(n) for n = 1..200</a>
%F A188183 Empirical: a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11).
%F A188183 Empirical: a(n) = 427*n^2/144 +155*n/32 +5501/1728+23*n^4/288 +115*n^3/144 -3*(-1)^n*n/32-15*(-1)^n/64 +A057077(n+1)/8 -2*A061347(n+1)/27; g.f.  -x*(12 +8*x +9*x^2 +7*x^3 +2*x^4 +7*x^5 +2*x^6 +3*x^7 -2*x^8 -5*x^9 +3*x^10) / ( (x^2+1) *(1+x+x^2) *(1+x)^2 *(x-1)^5 ). - R. J. Mathar, Mar 26 2011
%e A188183 Some solutions for n=5
%e A188183 .-5...-8...-7...-8...-6...-4...-8...-6...-8...-5...-8...-7...-6...-6...-8...-7
%e A188183 .-3...-3...-4...-6...-2...-3...-7...-5...-2...-3...-2...-4...-5...-5...-1...-6
%e A188183 .-1...-2....0....0...-1...-1....4...-2....2...-1....1...-2....2...-3....1....1
%e A188183 ..3....5....4....6....2....0....5....6....3....1....3....6....3....6....3....4
%e A188183 ..6....8....7....8....7....8....6....7....5....8....6....7....6....8....5....8
%K A188183 nonn
%O A188183 1,1
%A A188183 _R. H. Hardin_ Mar 23 2011