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

1,1

Links

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

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

Example

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

Crossrefs

Row 2 of A199832.

Cf. A000447, A016826.

Sequence in context: A063997 A355841 A187378 * A248964 A224086 A271013

Adjacent sequences: A199830 A199831 A199832 * A199834 A199835 A199836

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved