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A202969 Number of arrays of 9 integers in -n..n with sum zero and adjacent elements differing in absolute value.

%I A202969 #7 Jul 22 2025 16:54:32
%S A202969 6,5908,229714,3020170,21274708,102972822,384996502,1196677486,
%T A202969 3233011170,7831389294,17375280238,35875950626,69754837982,
%U A202969 128899962066,228011800792,388342150524,639825818930,1023746518060,1595913984468
%N A202969 Number of arrays of 9 integers in -n..n with sum zero and adjacent elements differing in absolute value.
%C A202969 Row 7 of A202962
%H A202969 R. H. Hardin, <a href="/A202969/b202969.txt">Table of n, a(n) for n = 1..210</a>
%F A202969 Empirical: a(n) = a(n-1) -a(n-2) +2*a(n-3) +2*a(n-5) -a(n-7) -a(n-8) -5*a(n-9) -a(n-10) -5*a(n-11) +4*a(n-12) -a(n-13) +9*a(n-14) +4*a(n-15) +7*a(n-16) +2*a(n-17) -2*a(n-18) -4*a(n-19) -11*a(n-20) -5*a(n-21) -11*a(n-22) +2*a(n-23) -2*a(n-24) +11*a(n-25) +5*a(n-26) +11*a(n-27) +4*a(n-28) +2*a(n-29) -2*a(n-30) -7*a(n-31) -4*a(n-32) -9*a(n-33) +a(n-34) -4*a(n-35) +5*a(n-36) +a(n-37) +5*a(n-38) +a(n-39) +a(n-40) -2*a(n-42) -2*a(n-44) +a(n-45) -a(n-46) +a(n-47)
%e A202969 Some solutions for n=2
%e A202969 ..1....1...-1...-1...-1....1...-1...-1...-1....0....0....2...-1...-1...-1....2
%e A202969 ..0....0....0....2....0....2...-2....0...-2...-1...-2....1....0....2....0....1
%e A202969 ..1...-1....2....0....2....0....0....2....1....0....1....2...-2...-1....1...-2
%e A202969 ..2...-2....1....2....1...-1....2....0....2...-1....2...-1...-1....2....2...-1
%e A202969 .-1....0....2...-1...-2...-2....0...-1...-1....2...-1....0....0...-1....1....2
%e A202969 .-2...-1...-1...-2....1...-1...-2....2....0....0....0...-1....2....0...-2....0
%e A202969 ..0....2....0...-1....0....2....0....1...-1....1....1....0....0....1....1....1
%e A202969 .-1...-1...-2....0...-1....1....2...-2....0....0...-2...-1....2...-2....0...-2
%e A202969 ..0....2...-1....1....0...-2....1...-1....2...-1....1...-2....0....0...-2...-1
%K A202969 nonn
%O A202969 1,1
%A A202969 _R. H. Hardin_ Dec 26 2011