A202254 Number of zero-sum -n..n arrays of 4 elements with adjacent element differences also in -n..n.

7, 31, 81, 171, 309, 509, 779, 1133, 1579, 2131, 2797, 3591, 4521, 5601, 6839, 8249, 9839, 11623, 13609, 15811, 18237, 20901, 23811, 26981, 30419, 34139, 38149, 42463, 47089, 52041, 57327, 62961, 68951, 75311, 82049, 89179, 96709, 104653, 113019

Offset: 1

Author

R. H. Hardin, Dec 14 2011

Keywords

• nonn

Comments

Row 4 of A202252.

Examples

			Some solutions for n=10:
   1  -1   1  -7  -7  -5   5   0   2  -6   4  -2  -2   9  -3  -9
   5  -8   7   1   1  -3   1  -5  -1  -2   6   3   1   1   1   1
  -1   1   1   6   5   1  -4   1  -2   8   0   4  -4   0   6   0
  -5   8  -9   0   1   7  -2   4   1   0 -10  -5   5 -10  -4   8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A202252.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).

Conjectures from Colin Barker, Mar 03 2018: (Start)

G.f.: x*(7 + 10*x + 2*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = (22*n^3 + 33*n^2 + 26*n + 12) / 12 for n even.

a(n) = (22*n^3 + 33*n^2 + 26*n + 3) / 12 for n odd.

(End)