cp's OEIS Frontend

A202257 Number of zero-sum -n..n arrays of 7 elements with adjacent element differences also in -n..n.

%I A202257 #12 Jul 22 2025 16:31:42
%S A202257 75,1415,10239,45523,150523,408211,960501,2031401,3953913,7200915,
%T A202257 12419753,20470827,32469879,49834303,74333103,108140939,153895771,
%U A202257 214760605,294488845,397493755,528921481,694728253,901761087,1157842693
%N A202257 Number of zero-sum -n..n arrays of 7 elements with adjacent element differences also in -n..n.
%C A202257 Row 7 of A202252
%H A202257 R. H. Hardin, <a href="/A202257/b202257.txt">Table of n, a(n) for n = 1..210</a>
%F A202257 Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -2*a(n-5) -a(n-6) +a(n-8) +a(n-9) +a(n-10) +a(n-12) -a(n-13) -a(n-15) -a(n-16) -a(n-17) +a(n-19) +2*a(n-20) +a(n-21) -a(n-22) -a(n-23) -a(n-24) +a(n-25).
%F A202257 Empirical: G.f. -x*(1340*x +x^24 +73*x^22 +805531*x^14 +1149240*x^12 +1199683*x^11 +1149241*x^10 +579582*x^7 +369388*x^6 +203491*x^5 +93421*x^4 +33794*x^3 +8749*x^2 +1008390*x^9 +805533*x^8 +1338*x^21 +203492*x^17 +8749*x^20 +33797*x^19 +93424*x^18 +369387*x^16 +579580*x^15 +1008389*x^13+75) / ( (x^2+1) *(x^4+x^3+x^2+x+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(1+x)^2 *(1+x+x^2)^2 *(x-1)^7 ). - R. J. Mathar, Dec 15 2011
%e A202257 Some solutions for n=4
%e A202257 .-1....0....4...-1....2....0....0....2....4...-3...-2...-1...-1....2...-3...-4
%e A202257 .-2...-3....1....0...-2....0...-4...-1....0...-4...-1...-4....0...-2...-2...-2
%e A202257 .-1...-1...-2...-2....1....0...-2...-2....2...-1....3....0....2...-2....0....1
%e A202257 ..3....0...-2...-1....1....0....2...-2...-1....1...-1....3....0....2....0....2
%e A202257 ..1...-1...-1....0...-2...-1....4....1...-2....4...-2....2....2....1....0....2
%e A202257 ..0....2....1....4...-1....0....2...-1...-2....0....0....2...-1...-2....1...-1
%e A202257 ..0....3...-1....0....1....1...-2....3...-1....3....3...-2...-2....1....4....2
%K A202257 nonn
%O A202257 1,1
%A A202257 _R. H. Hardin_ Dec 14 2011