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A202254
Number of zero-sum -n..n arrays of 4 elements with adjacent element differences also in -n..n.
2
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
1,1
COMMENTS
Row 4 of A202252.
LINKS
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)
EXAMPLE
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
CROSSREFS
Cf. A202252.
Sequence in context: A107005 A201477 A164621 * A305290 A262012 A118934
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 14 2011
STATUS
approved