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

1,2

Comments

Column 4 of A200057.

Links

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

Example

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

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

Crossrefs

Cf. A200057.

Sequence in context: A207099 A055064 A014347 * A164545 A199310 A316107

Adjacent sequences: A200050 A200051 A200052 * A200054 A200055 A200056

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved