cp's OEIS Frontend

A015818 Number of solutions of +- 1 +- 2 +- ... +- (n-1) +- n = 0 in which the partial sums +- 1 +- ... +- k (1<=k<=n) are all distinct.

%I A015818 #20 Dec 13 2018 16:17:16
%S A015818 1,0,0,2,2,0,0,2,2,0,0,10,14,0,0,36,40,0,0,134,258,0,0,702,1040,0,0,
%T A015818 4170,5996,0,0,23642,36616,0,0,140500,217002,0,0,852132,1374692,0,0,
%U A015818 5411800,8852230,0,0,35764246,56370054,0,0,232969442,376479130,0,0,1555855594,2534308444
%N A015818 Number of solutions of +- 1 +- 2 +- ... +- (n-1) +- n = 0 in which the partial sums +- 1 +- ... +- k (1<=k<=n) are all distinct.
%C A015818 If n==1 or 2 (mod 4) then a(n)=0.
%H A015818 Leroy Quet, <a href="http://groups.google.com/groups?selm=b4be2fdf.0211251643.65f368e6%40posting.google.com">Integers Arranged: Q & Puzzle</a>
%e A015818 For n=4 there are 2 solutions: +1-2-3+4=0 and -1+2+3-4=0.
%o A015818 (PARI) issol(i, n) = {b = binary(i); while(length(b) < n, b = concat(0, b)); if (! sum(k=1, n, if (b[k], k, -k)), vsp = []; lastnb = 0; for (j=1, n, vsp = Set(concat(vsp, sum(k=1, j, if (b[k], k, -k)))); if (#vsp == lastnb, return (0)); lastnb = #vsp;); return (1););}
%o A015818 a(n) = if ((!n) || ((n % 4) != 1) && ((n % 4) != 2), sum(i=0, 2^n-1, issol(i, n)));  \\ _Michel Marcus_, May 22 2014
%Y A015818 a(n) <= A063865(n).
%K A015818 nonn
%O A015818 0,4
%A A015818 _Leroy Quet_, _Christian G. Bower_ and _I. J. Kennedy_, Nov 26 2002
%E A015818 a(36)-a(46) from _Ray Chandler_, Nov 29 2008
%E A015818 a(47)-a(58) from _Sean A. Irvine_, Dec 13 2018