A201812 Number of arrays of 4 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.

19, 61, 151, 313, 571, 949, 1471, 2161, 3043, 4141, 5479, 7081, 8971, 11173, 13711, 16609, 19891, 23581, 27703, 32281, 37339, 42901, 48991, 55633, 62851, 70669, 79111, 88201, 97963, 108421, 119599, 131521, 144211, 157693, 171991, 187129, 203131

Offset: 1

Author

R. H. Hardin, Dec 05 2011

Keywords

• nonn

Comments

Row 4 of A201811.

Examples

			Some solutions for n=21:
  -6  15  -3  -8 -13   1  13  16  15 -15   3 -21  -6   8 -11   1
   9 -12   8   9   9  21  -2 -18  13   9  -7  12   3  20 -18  18
   4 -18  16 -17 -13 -14 -13   9 -20  21 -16  19 -11  -7  21 -15
  -7  15 -21  16  17  -8   2  -7  -8 -15  20 -10  14 -21   8  -4
		

Links

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

Crossrefs

Cf. A201811.

Formula

Empirical: a(n) = 4*n^3 + 14*n + 1.

Conjectures from Colin Barker, May 25 2018: (Start)

G.f.: x*(19 - 15*x + 21*x^2 - x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)