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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
1, 8, 36, 172, 840, 4172, 20978, 106674, 545698, 2811236, 14534258, 75522854, 393338058, 2056376914, 10767639532, 56550307652, 297322835298, 1567022163228, 8265441146830, 43685281805084, 231022736833454, 1223830782531260 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 09:43 EST 2021. Contains 349563 sequences. (Running on oeis4.)