cp's OEIS Frontend

A188126 Number of strictly increasing arrangements of 7 nonzero numbers in -(n+5)..(n+5) with sum zero.

%I A188126 #11 Nov 12 2020 05:16:46
%S A188126 42,152,426,1032,2216,4376,8044,13994,23210,37030,57086,85506,124816,
%T A188126 178186,249308,342708,463550,618042,813186,1057238,1359422,1730468,
%U A188126 2182232,2728362,3383832,4165678,5092482,6185216,7466594,8962070
%N A188126 Number of strictly increasing arrangements of 7 nonzero numbers in -(n+5)..(n+5) with sum zero.
%H A188126 R. H. Hardin, <a href="/A188126/b188126.txt">Table of n, a(n) for n = 1..200</a>
%F A188126 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 A188126    208637*n/12960 +413*(-1)^n/1152 +6403*n^3/1296 +355951*n^2/28800 +11*(-1)^n*n^2/384 +13*(-1)^n*n/96 +28669*n^4/25920 +709*n^5/5400 +841*n^6/129600 +6124649/777600 + (157*A049347(n)+74*A049347(n-1))/486 + 5*A128214(n+3)/81 +2*b(n)/25 + A057079(n+2)/18 -(-1)^(floor((n+1)/2))*A000034(n+1)/8 where b(n) is the 5-periodic sequence (-3,-1,-1,2,3,...) with offset 0.
%F A188126 Empirical: G.f. -2*x *(21 +34*x +61*x^2 +111*x^3 +152*x^4 +206*x^5 +217*x^6 +240*x^7 +212*x^8 +172*x^9 +120*x^10 +77*x^11 +36*x^12 +9*x^13 +11*x^14 -x^15 +4*x^16 +4*x^18 -8*x^20 +4*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 21 2011
%e A188126 Some solutions for n=6
%e A188126 -10..-10...-6...-7...-6..-11...-8..-10...-8..-11..-10...-9..-11..-11...-9...-9
%e A188126 .-9...-4...-3...-6...-5...-9...-7...-7...-7...-4...-7...-8...-9...-8...-6...-7
%e A188126 .-4...-2...-2...-4...-4...-3...-4...-6...-1...-3...-3...-3...-4...-4...-5...-4
%e A188126 ..4....2...-1....1...-1...-1...-3...-1....1...-2...-1...-1....1....3...-4...-2
%e A188126 ..5....3....1....3....3....4....5....6....3....1....1....5....2....4....7....4
%e A188126 ..6....4....2....6....4....9....6....8....4....8....9....6...10....6....8....8
%e A188126 ..8....7....9....7....9...11...11...10....8...11...11...10...11...10....9...10
%Y A188126 Row 7 of A188122.
%K A188126 nonn
%O A188126 1,1
%A A188126 _R. H. Hardin_, Mar 21 2011