A188212 Number of nondecreasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero.

18, 33, 55, 86, 126, 177, 241, 318, 410, 519, 645, 790, 956, 1143, 1353, 1588, 1848, 2135, 2451, 2796, 3172, 3581, 4023, 4500, 5014, 5565, 6155, 6786, 7458, 8173, 8933, 9738, 10590, 11491, 12441, 13442, 14496, 15603, 16765, 17984, 19260, 20595, 21991

Offset: 1

Author

R. H. Hardin, Mar 24 2011

Keywords

• nonn

Comments

Row 4 of A188211.

Examples

			Some solutions for n=3:
.-4...-5...-4...-5...-3...-1...-2...-2....0...-4...-3...-4...-2...-5...-4...-4
..1...-1...-1....1...-2...-1...-2...-1....0...-1...-3...-3...-2...-3...-4...-2
..1....2....1....2....0...-1....2....1....0....0....1....3....1....4....4....2
..2....4....4....2....5....3....2....2....0....5....5....4....3....4....4....4
		

Links

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

Crossrefs

Cf. A188211.

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).

Empirical g.f.: x*(18 - 21*x + 10*x^2 - 16*x^3 + 21*x^4 - 8*x^5) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Apr 27 2018