|
%I #11 Nov 20 2014 10:22:30
%S 1,8,36,172,840,4172,20978,106674,545698,2811236,14534258,75522854,
%T 393338058,2056376914,10767639532,56550307652,297322835298,
%U 1567022163228,8265441146830,43685281805084,231022736833454,1223830782531260
%N Number of -4..4 arrays X (0..n-1) of n elements with zero sum and elements alternately strictly increasing and strictly decreasing.
%C Column 4 of A200057.
%H R. H. Hardin, <a href="/A200053/b200053.txt">Table of n, a(n) for n = 1..200</a>
%e Some solutions for n=6:
%e .-2....2...-1...-3...-2....4....0...-1....0....2...-4....2...-1....0....0....1
%e ..2...-3....4....1....2....0....4....3...-2....0....2....4....2....4....2....0
%e ..1....2...-3....0...-1....3...-3...-1....4....2...-1....0...-3...-2...-2....2
%e ..4...-1....0....4....0...-3....3....4...-4...-3....1....1....1....1....1...-4
%e .-3....1...-2...-3...-3....0...-3...-3....2....1...-2...-4....0...-2...-3....4
%e .-2...-1....2....1....4...-4...-1...-2....0...-2....4...-3....1...-1....2...-3
%p T:= proc(a,n,s)
%p option remember;
%p if n = 1 then
%p if s = a then 1
%p else 0
%p fi
%p else
%p add(procname(-j,n-1,a-s), j=a+1..4)
%p fi
%p end proc:
%p A:= proc(n) 2*add(T(a,n,0),a=-4..4) end proc: A(1):= 1:
%p seq(A(n), n=1..30); # _Robert Israel_, Nov 19 2014
%Y Cf. A200057.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 13 2011
| 