A188338 Number of nondecreasing arrangements of 8 nonzero numbers in -(n+6)..(n+6) with sum zero

5142, 11200, 22563, 42593, 76251, 130453, 214784, 341988, 528926, 797248, 1174631, 1695625, 2403243, 3350003, 4599874, 6229576, 8330912, 11012320, 14401669, 18648073, 23925159, 30433213, 38402946, 48097954, 59819074, 73907174, 90748085

Offset

1,1

Comments

Row 8 of A188333

Links

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

Formula

Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-a(n-7)+a(n-9)+a(n-10)+a(n-12)-2*a(n-13)-2*a(n-16)+a(n-17)+a(n-19)+a(n-20)-a(n-22)+a(n-23)-a(n-24)-a(n-26)+2*a(n-28)-a(n-29).

Empirical: G.f. -x*(-5142 -916*x -2609*x^3 -2265*x^4 -5656*x^5 -2529*x^6 -5176*x^7 -6633*x^8 -5259*x^9 -2576*x^10 +3400*x^12 -110*x^13 +1064*x^14 +3324*x^15 -2452*x^16 -1012*x^17 -2864*x^18 -1943*x^19 +601*x^20 +1598*x^21 -1297*x^22 +2352*x^23 +675*x^24 +1715*x^25 -1323*x^26 -3484*x^27 +2132*x^28 -2108*x^11 -163*x^2) / ( (x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^8 ). - R. J. Mathar, Mar 28 2011

Example

Some solutions for n=6
-12..-12..-12...-6..-11...-9..-11..-11..-11..-11..-12...-9..-12..-12..-11..-12
.-9...-9..-10...-6...-7...-8...-4...-9..-10...-8...-8...-7...-7..-10..-10...-9
.-6...-6...-7...-5...-3...-8...-1...-8...-6...-2...-6...-5...-5...-8...-9...-9
.-4...-4...-4...-3....1...-2...-1...-3...-1...-2....3....2...-2...-6...-7...-7
..1...-4....3...-2....4....5....2....1....4...-2....3....2....5....5....6....6
..7...11....6....4....4....5....2....7....4....4....6....3....6...10....9....7
.11...12...12....9....6....6....6...11....8...10....7....7....6...10...11...12
.12...12...12....9....6...11....7...12...12...11....7....7....9...11...11...12

Crossrefs

Sequence in context: A237206 A230575 A251244 * A213701 A224462 A251679

Adjacent sequences: A188335 A188336 A188337 * A188339 A188340 A188341

Keyword

nonn

Author

R. H. Hardin Mar 28 2011

Status

approved