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A188126 Number of strictly increasing arrangements of 7 nonzero numbers in -(n+5)..(n+5) with sum zero 1
42, 152, 426, 1032, 2216, 4376, 8044, 13994, 23210, 37030, 57086, 85506, 124816, 178186, 249308, 342708, 463550, 618042, 813186, 1057238, 1359422, 1730468, 2182232, 2728362, 3383832, 4165678, 5092482, 6185216, 7466594, 8962070 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 7 of A188122

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)-2*a(n-7)+2*a(n-8)+a(n-9)-a(n-13)-2*a(n-14)+2*a(n-15)-a(n-16)+a(n-17)+a(n-19)-2*a(n-21)+a(n-22) =

   208637*n/12960 +413*(-1)^n/1152 +6403*n^3/1296 +355951*n^2/28800 +11*(-1)^n*n^2/384 +13*(-1)^n*n/96 +28669*n^4/25920 +709*n^5/5400 +841*n^6/129600 +6124649/777600 + (157*A049347(n)+74*A049347(n-1))/486 + 5*A128214(n+3)/81 +2*b(n)/25 + A057079(n+2)/18 -(-1)^(floor((n+1)/2))*A000034(n+1)/8 where b(n) is the 5-periodic sequence (-3,-1,-1,2,3,...) with offset 0.

Empirical: G.f. -2*x *(21 +34*x +61*x^2 +111*x^3 +152*x^4 +206*x^5 +217*x^6 +240*x^7 +212*x^8 +172*x^9 +120*x^10 +77*x^11 +36*x^12 +9*x^13 +11*x^14 -x^15 +4*x^16 +4*x^18 -8*x^20 +4*x^21) / ( (x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^7 ). - R. J. Mathar, Mar 21 2011

EXAMPLE

Some solutions for n=6

-10..-10...-6...-7...-6..-11...-8..-10...-8..-11..-10...-9..-11..-11...-9...-9

.-9...-4...-3...-6...-5...-9...-7...-7...-7...-4...-7...-8...-9...-8...-6...-7

.-4...-2...-2...-4...-4...-3...-4...-6...-1...-3...-3...-3...-4...-4...-5...-4

..4....2...-1....1...-1...-1...-3...-1....1...-2...-1...-1....1....3...-4...-2

..5....3....1....3....3....4....5....6....3....1....1....5....2....4....7....4

..6....4....2....6....4....9....6....8....4....8....9....6...10....6....8....8

..8....7....9....7....9...11...11...10....8...11...11...10...11...10....9...10

CROSSREFS

Sequence in context: A230932 A224954 A158479 * A189500 A075289 A193571

Adjacent sequences:  A188123 A188124 A188125 * A188127 A188128 A188129

KEYWORD

nonn

AUTHOR

R. H. Hardin Mar 21 2011

STATUS

approved

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.