A202079 - OEIS

%I #9 May 27 2018 06:56:57

%S 12,524,5832,34632,142692,462436,1264272,3044496,6644604,13406844,

%T 25370840,45516120,78055380,128783316,205485856,318414624,480831468,

%U 709627884,1026024168,1456353128,2032933188,2795035716,3789951408

%N Number of arrays of 8 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

%C Row 6 of A202076.

%H R. H. Hardin, <a href="/A202079/b202079.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8).

%F Empirical g.f.: 4*x*(1 + x)*(3 + 104*x + 390*x^2 + 104*x^3 + 3*x^4) / (1 - x)^8. - _Colin Barker_, May 27 2018

%e Some solutions for n=3:

%e .-3...-2....1...-3....2....2....1....1...-2....2....3...-2....1...-3....3....0

%e ..0....1...-2....0....3....1....0...-2....3....3...-2....3....2....0...-2...-1

%e ..3....2...-1....1....0...-2...-3...-3....2...-2....1....2....3....3...-3....0

%e ..0...-1...-2....2...-3....1....0...-2...-1...-3....0...-1...-2...-2....2...-1

%e ..1...-2...-1....3...-2...-2....3....3....2....2....1...-2...-3....3....1....0

%e .-2...-3....0...-2...-1...-1...-2....2...-3...-3....2....1....0...-2....0...-3

%e ..1....2....3...-3...-2....2....1....3....2...-2...-3...-2...-3...-1...-3....2

%e ..0....3....2....2....3...-1....0...-2...-3....3...-2....1....2....2....2....3

%Y Cf. A202076.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2011