This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A175032 #39 Nov 12 2022 08:29:35
%S A175032 0,0,1,3,6,1,4,8,0,4,9,15,3,9,16,1,8,16,25,6,15,25,3,13,24,36,10,22,
%T A175032 35,6,19,33,1,15,30,46,10,26,43,4,21,39,58,15,34,54,8,28,49,0,21,43,
%U A175032 66,13,36,60,4,28,53,79,19,45,72,9,36,64,93,26,55,85,15,45,76,3,34,66,99,22
%N A175032 a(n) is the difference between the n-th triangular number and the next perfect square.
%C A175032 All terms are from {0} U A175035. No terms are from A175034.
%C A175032 The sequence consists of ascending runs of length 3 or 4. The first run starts at n = 1 and thereafter the k-th run starts at n = A214858(k - 1). - _John Tyler Rascoe_, Nov 05 2022
%H A175032 Seiichi Manyama, <a href="/A175032/b175032.txt">Table of n, a(n) for n = 0..10000</a>
%F A175032 a(n) = (ceiling(sqrt(n*(n+1)/2)))^2 - n*(n+1)/2. - _Ctibor O. Zizka_, Nov 09 2009
%F A175032 a(n) = A080819(n) - A000217(n). - _R. J. Mathar_, Aug 24 2010
%t A175032 Ceiling[Sqrt[#]]^2-#&/@Accumulate[Range[0,80]] (* _Harvey P. Dale_, Aug 25 2013 *)
%o A175032 (PARI) a(n) = my(t=n*(n+1)/2); if (issquare(t), 0, (sqrtint(t)+1)^2 - t); \\ _Michel Marcus_, Nov 06 2022
%Y A175032 Cf. A001109, A214858.
%Y A175032 Cf. A000217, A080819.
%Y A175032 Cf. A175034, A175035.
%Y A175032 Cf. sequences where a(m)=k: A001108 (0), A006451 (1), A154138 (3), A154139 (4), A154140 (6), A154141 (8), A154142 (9), A154143 (10), A154144 (13), A154145 (15), A154146 (16), A154147 (19), A154148 (21), A154149 (22), A154150(24), A154151 (25), A154151 (26), A154153(28), A154154 (30).
%K A175032 easy,nonn,look
%O A175032 0,4
%A A175032 _Ctibor O. Zizka_, Nov 09 2009
%E A175032 Erroneous formula variant deleted and offset set to zero by _R. J. Mathar_, Aug 24 2010