A076042 a(0) = 0; thereafter a(n) = a(n-1) + n^2 if a(n-1) < n^2, otherwise a(n) = a(n-1) - n^2.

0, 1, 5, 14, 30, 5, 41, 90, 26, 107, 7, 128, 272, 103, 299, 74, 330, 41, 365, 4, 404, 845, 361, 890, 314, 939, 263, 992, 208, 1049, 149, 1110, 86, 1175, 19, 1244, 2540, 1171, 2615, 1094, 2694, 1013, 2777, 928, 2864, 839, 2955, 746, 3050, 649, 3149

Offset: 0

Author

Amarnath Murthy, Oct 29 2002

Keywords

• nonn
• look

Comments

Does not return to zero within first 2^25000 =~ 10^7525 terms. Define an epoch as an addition followed by a sequence of (addition, subtraction) pairs. The first epoch has length 1 (+), the second 3 (++-), the third 5 (++-+-), and so forth (cf. A324792). The epoch lengths increase geometrically by about the square root of 3, and the value at the end of each epoch is the low value in the epoch. These observations lead to the Python program given. - Tomas Rokicki, Aug 31 2019

Using the Maple program in A324791, I confirmed that a(n) != 0 for 0 < n < 10^2394. See the a- and b-files in A325056 and A324791. - N. J. A. Sloane, Oct 03 2019

'Easy Recamán transform' of the squares. - Daniel Forgues, Oct 25 2019

Links

• Tomas Rokicki, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A076039, A003462, A076041, A046901.

See also A325056, A324791, A324792.

Cf. A053461 ('Recamán transform' of the squares).

Cf. A000290, A008344, A008345.

Programs

Maple

a:= proc(n) option remember; `if`(n<0, 0,
      ((s, t)-> s+`if`(sAlois P. Heinz, Jan 11 2020

Mathematica

a[0] = 0;
a[n_] := a[n] = a[n-1] + If[a[n-1] < n^2, n^2, -n^2];
a /@ Range[0, 50] (* Jean-François Alcover, Apr 11 2020 *)

PARI

v=vector(50); v[1]=1; for(n=2,50,if(v[n-1]
				

Extensions

More terms from Ralf Stephan, Mar 20 2003

a(0)=0 prepended, at the suggestion of Allan C. Wechsler, by N. J. A. Sloane, Aug 31 2019

Offset set to 0, to cohere with previous action of N. J. A. Sloane, by Allan C. Wechsler, Sep 08 2019