A200183 - OEIS

%I #8 May 19 2018 09:49:30

%S 2,12,15,24,31,48,53,74,83,108,119,148,159,196,209,246,263,308,323,

%T 372,391,444,465,522,543,608,631,696,723,796,821,898,927,1008,1039,

%U 1124,1155,1248,1281,1374,1411,1512,1547,1652,1691,1800,1841,1954,1995,2116,2159

%N Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two consecutive declines, no adjacent equal elements, and no element more than one greater than the previous (random base sawtooth pattern).

%C Row 5 of A200181.

%H R. H. Hardin, <a href="/A200183/b200183.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-5) -a(n-6) -a(n-7) +a(n-9) for n>10.

%F Empirical g.f.: x*(2 + 12*x + 13*x^2 + 10*x^3 + 2*x^4 - x^5 - 3*x^6 + 2*x^8 + x^9) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, May 19 2018

%e Some solutions for n=6:

%e ..0....6....5....5....4....3....0....5....2....2....2....1....2....4....2....6

%e ..1....1...-2....6...-2...-1...-1....6....3....3....3....2...-1....1....3...-1

%e ..2....2...-1...-3...-1....0....0...-4...-1....4...-2...-2....0....2....0....0

%e .-2...-5....0...-2....0....1....1...-3....0...-5...-1...-1....1...-4....1...-3

%e .-1...-4...-2...-6...-1...-3....0...-4...-4...-4...-2....0...-2...-3...-6...-2

%Y Cf. A200181.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2011