cp's OEIS Frontend

A188127 Number of strictly increasing arrangements of 8 nonzero numbers in -(n+6)..(n+6) with sum zero.

%I A188127 #11 Jul 22 2025 11:00:36
%S A188127 137,484,1398,3528,7970,16547,32035,58595,102113,170844,275878,432018,
%T A188127 658432,979785,1427065,2039067,2863403,3958322,5393994,7254686,
%U A188127 9640296,12669003,16479033,21231771,27113883,34340884,43159574,53852210,66739242
%N A188127 Number of strictly increasing arrangements of 8 nonzero numbers in -(n+6)..(n+6) with sum zero.
%C A188127 Row 8 of A188122
%H A188127 R. H. Hardin, <a href="/A188127/b188127.txt">Table of n, a(n) for n = 1..200</a>
%F A188127 Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-a(n-7)+a(n-9)+a(n-10)+a(n-12)-2*a(n-13)-2*a(n-16)+a(n-17)+a(n-19)+a(n-20)-a(n-22)+a(n-23)-a(n-24)-a(n-26)+2*a(n-28)-a(n-29).
%F A188127 Empirical: G.f. -x*(-137 -210*x -3284*x^12 -869*x^3 -1398*x^4 -2142*x^5 -2816*x^6 -3546*x^7 -4084*x^8 -4269*x^10 -3951*x^11 -2644*x^13 -1892*x^14 -1202*x^15 -768*x^16 -389*x^17 -202*x^18 -87*x^19 -5*x^20 +20*x^21 -26*x^22 +32*x^23 +5*x^24 +29*x^25 -9*x^26 -57*x^27 +31*x^28 -4356*x^9 -430*x^2) / ( (x^2-x+1) *(x^5-1) *(x^7-1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Mar 21 2011
%e A188127 Some solutions for n=6
%e A188127 -12..-11..-12...-8..-10..-12...-9..-10...-6..-12...-8..-10..-12..-10..-12..-11
%e A188127 .-9..-10...-7...-7...-7..-11...-8...-8...-5...-9...-7...-6...-4...-8...-9...-7
%e A188127 .-8...-2...-6...-4...-4...-3...-7...-7...-2...-3...-3...-3...-3...-5...-7...-5
%e A188127 .-2....1...-2...-3...-3...-2...-6...-5...-1...-2...-1...-1....1...-3....2...-4
%e A188127 ..5....2...-1....3...-2....1....1....4....1....1....1....1....2....1....4...-2
%e A188127 ..7....3....5....4....5....4....6....7....2....4....3....2....3....5....5....8
%e A188127 ..9....5...11....7...10...11...11....8....5...10....4....5....6....8....7....9
%e A188127 .10...12...12....8...11...12...12...11....6...11...11...12....7...12...10...12
%K A188127 nonn
%O A188127 1,1
%A A188127 _R. H. Hardin_ Mar 21 2011