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