A193697 Number of arrays of -3..3 integers x(1..n) with every x(i) in a subsequence of length 1, 2 or 3 with sum zero.

1, 7, 43, 181, 827, 3773, 17197, 78407, 357403, 1629369, 7428007, 33862711, 154372795, 703751937, 3208252657, 14625730979, 66675552791, 303959466209, 1385685646663, 6317041957501, 28798031581467, 131284013681727, 598495497977845, 2728411869163663, 12438241145358561

Offset: 1

Author

R. H. Hardin, Aug 02 2011

Keywords

• nonn

Examples

			Some solutions for n=6:
..3...-2....0....2...-3....1....1...-2....2...-3...-3...-2....0...-3....3....3
.-3....0....0...-1....2...-3....1....2....0....1....0....2....1....0...-3...-3
..2....2....0...-1....1....2...-2....0...-2....2....3....0....2....3....2...-1
..1...-3...-3....1....2...-2....1....1...-1...-2...-2...-1...-3....1...-2....1
..1....1....3...-1...-3....2....1...-3....2....0....0....1....2...-2...-1....2
.-2...-1...-3....0....1....0...-2....2...-1....0....2...-1....1....1....3...-2
		

Links

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

Crossrefs

Column 3 of A193702.

Formula

Empirical: a(n) = 4*a(n-1) +a(n-2) -a(n-3) +21*a(n-4) +47*a(n-5) +60*a(n-6) +155*a(n-7) +255*a(n-8) +386*a(n-9) +623*a(n-10) +899*a(n-11) +976*a(n-12) +972*a(n-13) +664*a(n-14) +119*a(n-15) -414*a(n-16) -754*a(n-17) -970*a(n-18) -886*a(n-19) -786*a(n-20) -580*a(n-21) -358*a(n-22) -109*a(n-23) +40*a(n-24) +116*a(n-25) +100*a(n-26) +66*a(n-27) +37*a(n-28) +19*a(n-29) +6*a(n-30) +a(n-31).