cp's OEIS Frontend

A300307 Number of solutions to 1 +- 3 +- 6 +- ... +- n*(n+1)/2 == 0 mod n.

%I A300307 #28 Mar 05 2018 05:02:36
%S A300307 1,2,0,4,4,16,12,32,20,112,88,384,308,1264,1056,4096,3852,15120,13820,
%T A300307 52608,49824,190848,182356,704512,671540,2582128,2475220,9615744,
%U A300307 9256428,35868672,34636840,134217728,130021392,505292976,491156304,1909836416,1857282536
%N A300307 Number of solutions to 1 +- 3 +- 6 +- ... +- n*(n+1)/2 == 0 mod n.
%H A300307 Seiichi Manyama, <a href="/A300307/b300307.txt">Table of n, a(n) for n = 1..2^11</a>
%F A300307 a(2^n) = 2^A000325(n) for n>0 (conjectured).
%e A300307 Solutions for n = 7:
%e A300307 ------------------------------
%e A300307 1 +3 +6 +10 +15 +21 +28 =  84.
%e A300307 1 +3 +6 +10 +15 +21 -28 =  28.
%e A300307 1 +3 +6 +10 +15 -21 +28 =  42.
%e A300307 1 +3 +6 +10 +15 -21 -28 = -14.
%e A300307 1 +3 -6 +10 -15 +21 +28 =  42.
%e A300307 1 +3 -6 +10 -15 +21 -28 = -14.
%e A300307 1 +3 -6 +10 -15 -21 +28 =   0.
%e A300307 1 +3 -6 +10 -15 -21 -28 = -56.
%e A300307 1 -3 +6 -10 -15 +21 +28 =  28.
%e A300307 1 -3 +6 -10 -15 +21 -28 = -28.
%e A300307 1 -3 +6 -10 -15 -21 +28 = -14.
%e A300307 1 -3 +6 -10 -15 -21 -28 = -70.
%o A300307 (Ruby)
%o A300307 def A(n)
%o A300307   ary = [1] + Array.new(n - 1, 0)
%o A300307   (1..n).each{|i|
%o A300307     it = i * (i + 1)
%o A300307     a = ary.clone
%o A300307     (0..n - 1).each{|j| a[(j + it) % n] += ary[j]}
%o A300307     ary = a
%o A300307   }
%o A300307   ary[(n * (n + 1) * (n + 2) / 6) % n] / 2
%o A300307 end
%o A300307 def A300307(n)
%o A300307   (1..n).map{|i| A(i)}
%o A300307 end
%o A300307 p A300307(100)
%Y A300307 Cf. A000079, A000217, A000325, A058498, A300190, A300218.
%K A300307 nonn
%O A300307 1,2
%A A300307 _Seiichi Manyama_, Mar 02 2018