

A175032


a(n) is the difference between the nth 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
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OFFSET

0,4


COMMENTS

The sequence consists of ascending runs of length 3 or 4. The first run starts at n = 1 and thereafter the kth 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


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).


KEYWORD



AUTHOR



EXTENSIONS

Erroneous formula variant deleted and offset set to zero by R. J. Mathar, Aug 24 2010


STATUS

approved



