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

1,1

Comments

Row 4 of A188211.

Links

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

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

Example

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

Crossrefs

Cf. A188211.

Sequence in context: A045556 A344017 A049731 * A093478 A214465 A296860

Adjacent sequences: A188209 A188210 A188211 * A188213 A188214 A188215

Keyword

nonn

Author

R. H. Hardin, Mar 24 2011

Status

approved