The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A175032 a(n) is the difference between the n-th triangular number and the next perfect square. 2
 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, 35, 6, 19, 33, 1, 15, 30, 46, 10, 26, 43, 4, 21, 39, 58, 15, 34, 54, 8, 28, 49, 0, 21, 43, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS All terms are from {0} U A175035. No terms are from A175034. 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 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA a(n) = (ceiling(sqrt(n*(n+1)/2)))^2 - n*(n+1)/2. - Ctibor O. Zizka, Nov 09 2009 a(n) = A080819(n) - A000217(n). - R. J. Mathar, Aug 24 2010 MATHEMATICA Ceiling[Sqrt[#]]^2-#&/@Accumulate[Range[0, 80]] (* Harvey P. Dale, Aug 25 2013 *) PROG (PARI) a(n) = my(t=n*(n+1)/2); if (issquare(t), 0, (sqrtint(t)+1)^2 - t); \\ Michel Marcus, Nov 06 2022 CROSSREFS Cf. A001109, A214858. Cf. A000217, A080819. Cf. A175034, A175035. 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). Sequence in context: A181099 A163327 A338460 * A078768 A307281 A089078 Adjacent sequences: A175029 A175030 A175031 * A175033 A175034 A175035 KEYWORD easy,nonn,look AUTHOR Ctibor O. Zizka, Nov 09 2009 EXTENSIONS Erroneous formula variant deleted and offset set to zero by R. J. Mathar, Aug 24 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 10:24 EDT 2024. Contains 373543 sequences. (Running on oeis4.)