A188239 Number of nondecreasing arrangements of 6 numbers in -(n+4)..(n+4) with sum zero and not more than two numbers equal.

245, 527, 1019, 1818, 3047, 4859, 7435, 10994, 15791, 22121, 30323, 40782, 53931, 70257, 90301, 114662, 143999, 179037, 220565, 269444, 326607, 393061, 469893, 558272, 659449, 774765, 905649, 1053624, 1220309, 1407423, 1616785, 1850320

Offset

1,1

Comments

Row 6 of A188236.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 2*a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) - a(n-10) - 2*a(n-11) + 3*a(n-12) - a(n-13).

Empirical g.f.: x*(245 - 208*x - 72*x^2 + 60*x^3 + 158*x^4 - 117*x^5 - 39*x^6 + 188*x^7 - 42*x^8 - 140*x^9 - 110*x^10 + 263*x^11 - 98*x^12) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 27 2018

Example

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

Crossrefs

Cf. A188236.

Sequence in context: A129210 A137521 A257781 * A132830 A350421 A236887

Adjacent sequences: A188236 A188237 A188238 * A188240 A188241 A188242

Keyword

nonn

Author

R. H. Hardin, Mar 24 2011

Status

approved