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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
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. 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
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

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