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A202256 Number of zero-sum -n..n arrays of 6 elements with adjacent element differences also in -n..n.

%I A202256 #9 Jul 22 2025 16:31:35
%S A202256 33,387,2003,6963,18841,43293,88301,164873,287151,473293,745359,
%T A202256 1130441,1660283,2372685,3310839,4525059,6071723,8015439,10427561,
%U A202256 13388757,16987109,21321159,26497455,32634197,39858185,48309035,58135563,69500619
%N A202256 Number of zero-sum -n..n arrays of 6 elements with adjacent element differences also in -n..n.
%C A202256 Row 6 of A202252
%H A202256 R. H. Hardin, <a href="/A202256/b202256.txt">Table of n, a(n) for n = 1..210</a>
%F A202256 Empirical: a(n) = 2*a(n-2) +2*a(n-3) -3*a(n-5) -3*a(n-6) -2*a(n-7) +a(n-8) +4*a(n-9) +4*a(n-10) +a(n-11) -2*a(n-12) -3*a(n-13) -3*a(n-14) +2*a(n-16) +2*a(n-17) -a(n-19).
%F A202256 Empirical: G.f. -x*(-33 -387*x -1937*x^2 -6123*x^3 -14061*x^4 -25460*x^5 -37953*x^6 -47841*x^7 -51602*x^8 -47844*x^9 -37956*x^10 -25461*x^11 -14061*x^12 -6120*x^13 -1935*x^14 -387*x^15 -35*x^16 -x^17+x^18) / ( (x^2+1) *(x^4+x^3+x^2+x+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Dec 15 2011
%e A202256 Some solutions for n=7
%e A202256 ..6...-7...-5...-5....2....6....2...-1...-1....0...-6...-4....5....1....1...-6
%e A202256 ..0....0....1....2...-1....1...-3...-5...-2...-4...-5...-5....4....0....2...-7
%e A202256 .-3....4....2...-2....6....0...-1...-1....0....1....2...-2...-2...-3...-1...-1
%e A202256 .-3....6....1....3...-1...-3...-1....1....3....1....1....5...-6....1....3....4
%e A202256 .-1....2....3....0...-6...-1....1....4....0...-1....5....4...-4....1....1....6
%e A202256 ..1...-5...-2....2....0...-3....2....2....0....3....3....2....3....0...-6....4
%K A202256 nonn
%O A202256 1,1
%A A202256 _R. H. Hardin_ Dec 14 2011