A199833 Number of -n..n arrays of 4 elements with zero sum and no two neighbors summing to zero.

4, 40, 140, 336, 660, 1144, 1820, 2720, 3876, 5320, 7084, 9200, 11700, 14616, 17980, 21824, 26180, 31080, 36556, 42640, 49364, 56760, 64860, 73696, 83300, 93704, 104940, 117040, 130036, 143960, 158844, 174720, 191620, 209576, 228620, 248784

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Examples

			Some solutions for n=3:
   0  -3  -3   0   0   0  -1   1   1  -1   0   0  -3  -2  -1  -2
  -2   2  -1   3   1   1   0   1  -2   2  -2   1   2   1  -3   0
   3   3   2   0   2   1  -1  -3   1   0   0   0  -1  -2   1   1
  -1  -2   2  -3  -3  -2   2   1   0  -1   2  -1   2   3   3   1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Row 2 of A199832.

Cf. A000447, A016826.

Formula

Empirical: a(n) = (16/3)*n^3 - (4/3)*n = 4*A000447(n).

Empirical: G.f.: 4*x*(1+6*x+x^2) / (x-1)^4 . - R. J. Mathar, Aug 01 2014

Empirical: partial sums of A016826. - Sean A. Irvine, Jul 13 2022