A193704 Number of arrays of -2..2 integers x(1..n) with every x(i) in a subsequence of length 1, 2, 3 or 4 with sum zero.

1, 5, 23, 119, 489, 1987, 8043, 32599, 132713, 540913, 2205225, 8989861, 36646831, 149381195, 608893037, 2481878351, 10116219555, 41234080525, 168071970545, 685070063741, 2792383408313, 11381911805631, 46393311136175

Offset

1,2

Comments

Column 2 of A193710.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +4*a(n-2) +a(n-3) -10*a(n-4) +10*a(n-5) +97*a(n-6) +202*a(n-7) +211*a(n-8) +184*a(n-9) +359*a(n-10) +772*a(n-11) +1020*a(n-12) +803*a(n-13) +4*a(n-14) -618*a(n-15) +491*a(n-16) +3674*a(n-17) +6991*a(n-18) +5747*a(n-19) -3079*a(n-20) -14036*a(n-21) -19019*a(n-22) -14576*a(n-23) -5701*a(n-24) +980*a(n-25) -3128*a(n-26) -12159*a(n-27) -19677*a(n-28) -21113*a(n-29) -11499*a(n-30) -3507*a(n-31) +1809*a(n-32) +1619*a(n-33) -5989*a(n-34) -11700*a(n-35) -12527*a(n-36) -9260*a(n-37) -4560*a(n-38) +1240*a(n-39) +7*a(n-40) +712*a(n-41) -65*a(n-42) -1846*a(n-43) -115*a(n-44) -1095*a(n-45) -734*a(n-46) -22*a(n-47) -851*a(n-48) +140*a(n-49) +121*a(n-50) +246*a(n-51) +370*a(n-52) +66*a(n-53) +7*a(n-54) -99*a(n-55) -84*a(n-56) -12*a(n-57).

Example

Some solutions for n=6
..2....2....0....0...-1....2...-1...-2....2....2....1....2...-1....0....1...-1
.-1....1....1....2....2...-2....2....0....1....0....1....1...-1....1...-1....2
.-1...-1...-1...-1....1....0...-1....1...-1...-1...-2...-2....0....2....1...-1
..2...-2....2...-1...-2....0....0....1...-2...-1...-1...-1....2...-1...-2...-1
..0....0....0...-1....2...-2...-1....2....2...-1....0....0...-2...-2...-1....0
..0....0...-2....2....0....2....2...-2....0....2....1....0....0....1....2....1

Crossrefs

Cf. A193710.

Sequence in context: A167248 A321798 A005393 * A294356 A162815 A351756

Adjacent sequences: A193701 A193702 A193703 * A193705 A193706 A193707

Keyword

nonn

Author

R. H. Hardin, Aug 02 2011

Status

approved