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A188182 Number of strictly increasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero.

%I A188182 #9 Jul 22 2025 11:01:46
%S A188182 5,12,24,43,69,104,150,207,277,362,462,579,715,870,1046,1245,1467,
%T A188182 1714,1988,2289,2619,2980,3372,3797,4257,4752,5284,5855,6465,7116,
%U A188182 7810,8547,9329,10158,11034,11959,12935,13962,15042,16177,17367,18614,19920,21285
%N A188182 Number of strictly increasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero.
%C A188182 Row 4 of A188181
%H A188182 R. H. Hardin, <a href="/A188182/b188182.txt">Table of n, a(n) for n = 1..200</a>
%F A188182 Empirical: a(n)=3*a(n-1)-3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6).
%F A188182 Empirical: a(n) = (n+1)*(4*n^2+17*n+22)/18 -2 *A049347(n)/9; g.f. -x*(-5+3*x-3*x^2+3*x^3-3*x^4+x^5) / ( (1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Mar 26 2011
%e A188182 Some solutions for n=5
%e A188182 .-6...-7...-6...-5...-3...-7...-4...-5...-4...-5...-6...-2...-6...-6...-7...-4
%e A188182 .-4....0...-1...-4....0...-1...-3...-3...-2...-2...-5...-1...-3...-3....0...-3
%e A188182 ..3....1....3....4....1....2....0....1....2....2....5....0....3....2....3....1
%e A188182 ..7....6....4....5....2....6....7....7....4....5....6....3....6....7....4....6
%K A188182 nonn
%O A188182 1,1
%A A188182 _R. H. Hardin_ Mar 23 2011