cp's OEIS Frontend

A188185 Number of strictly increasing arrangements of 7 numbers in -(n+5)..(n+5) with sum zero.

%I A188185 #9 Jul 22 2025 11:02:08
%S A188185 94,289,734,1656,3370,6375,11322,19138,30982,48417,73316,108108,
%T A188185 155646,219489,303748,413442,554256,733005,957332,1236222,1579666,
%U A188185 1999265,2507780,3119876,3851588,4721127,5748298,6955424,8366614,10008857
%N A188185 Number of strictly increasing arrangements of 7 numbers in -(n+5)..(n+5) with sum zero.
%C A188185 Row 7 of A188181
%H A188185 R. H. Hardin, <a href="/A188185/b188185.txt">Table of n, a(n) for n = 1..200</a>
%F A188185 Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-2*a(n-7)+2*a(n-8)+a(n-9)-a(n-13)-2*a(n-14)+2*a(n-15)-a(n-16)+a(n-17)+a(n-19)-2*a(n-21)+a(n-22).
%F A188185 Empirical: G.f.  -x*(94 +101*x +156*x^2 +282*x^3 +347*x^4 +463*x^5 +423*x^6 +497*x^7 +393*x^8 +285*x^9 +180*x^10 +99*x^11 +17*x^12 -25*x^13 +47*x^14 -19*x^15 +25*x^16 +4*x^17 +22*x^18 -7*x^19 -44*x^20 +24*x^21) / ( (x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^7 ). - R. J. Mathar, Mar 26 2011
%e A188185 Some solutions for n=5
%e A188185 .-9...-7...-9..-10..-10..-10...-7...-9..-10..-10..-10..-10..-10...-9...-7..-10
%e A188185 .-7...-4...-7...-6...-7...-4...-6...-7...-3...-8...-5...-8...-8...-6...-6...-6
%e A188185 .-3...-2...-2...-5...-3...-3...-4...-4...-1...-2...-1...-7...-5...-1...-3...-5
%e A188185 .-1...-1....0....2....2...-1...-3....1....0...-1....1....3...-1....1...-2....1
%e A188185 ..5....0....3....4....3....3....4....2....1....5....2....6....6....2....0....4
%e A188185 ..6....6....6....7....6....7....7....8....4....7....4....7....8....4....8....7
%e A188185 ..9....8....9....8....9....8....9....9....9....9....9....9...10....9...10....9
%K A188185 nonn
%O A188185 1,1
%A A188185 _R. H. Hardin_ Mar 23 2011