A199707 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two neighbors equal.
14, 200, 892, 2734, 6504, 13324, 24394, 41344, 65788, 99858, 145596, 205612, 282386, 379036, 498440, 644218, 819692, 1028960, 1275766, 1564716, 1899968, 2286630, 2729288, 3233528, 3804374, 4447920, 5169588, 5975974, 6872944, 7867572, 8966146
Offset: 1
Keywords
Examples
Some solutions for n=5: .-5...-1...-3...-4....4....1...-3...-1....5....0...-4....1....4....0....2....1 ..0....0....1...-3....1....3....1....2...-3...-2...-3...-2....0....2....3...-3 .-3...-4....2....3...-3....1...-4...-1...-1....5....1...-3...-3....4...-5....5 ..3....2...-5....1...-4...-5....2....1...-3...-2....2....4....1...-4....4....1 ..5....3....5....3....2....0....4...-1....2...-1....4....0...-2...-2...-4...-4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A199704.
Formula
Empirical: a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11).
Empirical g.f.: 2*x*(7 + 86*x + 246*x^2 + 482*x^3 + 618*x^4 + 618*x^5 + 426*x^6 + 222*x^7 + 47*x^8 + 8*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 16 2018
Comments