A200053 Number of -4..4 arrays X (0..n-1) of n elements with zero sum and elements alternately strictly increasing and strictly decreasing.

1, 8, 36, 172, 840, 4172, 20978, 106674, 545698, 2811236, 14534258, 75522854, 393338058, 2056376914, 10767639532, 56550307652, 297322835298, 1567022163228, 8265441146830, 43685281805084, 231022736833454, 1223830782531260

Offset: 1

Author

R. H. Hardin, Nov 13 2011

Keywords

• nonn

Comments

Column 4 of A200057.

Examples

			Some solutions for n=6:
.-2....2...-1...-3...-2....4....0...-1....0....2...-4....2...-1....0....0....1
..2...-3....4....1....2....0....4....3...-2....0....2....4....2....4....2....0
..1....2...-3....0...-1....3...-3...-1....4....2...-1....0...-3...-2...-2....2
..4...-1....0....4....0...-3....3....4...-4...-3....1....1....1....1....1...-4
.-3....1...-2...-3...-3....0...-3...-3....2....1...-2...-4....0...-2...-3....4
.-2...-1....2....1....4...-4...-1...-2....0...-2....4...-3....1...-1....2...-3
		

Links

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

Crossrefs

Cf. A200057.

Programs

Maple

T:= proc(a,n,s)
   option remember;
   if n = 1 then
      if s = a then 1
      else 0
      fi
   else
     add(procname(-j,n-1,a-s), j=a+1..4)
   fi
end proc:
A:= proc(n)  2*add(T(a,n,0),a=-4..4) end proc: A(1):= 1:
seq(A(n), n=1..30); # Robert Israel, Nov 19 2014