A373330 a(n) is the difference between T = A000217(n^2) and the greatest square not exceeding T.

0, 0, 1, 9, 15, 1, 41, 0, 55, 72, 9, 156, 36, 204, 262, 144, 135, 289, 209, 316, 111, 117, 406, 309, 527, 261, 342, 860, 804, 36, 954, 1200, 624, 605, 1257, 969, 1400, 741, 849, 1856, 1639, 0, 1721, 2076, 855, 701, 1770, 1101, 1719, 397, 426, 1980, 1416, 2449, 1142

Offset

0,4

Links

Michael De Vlieger, Table of n, a(n) for n = 0..9998

Hugo Pfoertner, Logarithmic plot of a(n) vs n, n <= 10^5, lower envelope of terms > 0 shown in red, zoom for details.

Formula

a(n) = A000217(n^2) - A373329(n)^2.

a(A002315(n)) = 0.

Mathematica

Array[PolygonalNumber[#^2] - Floor[Sqrt[(#^4 + #^2)/2]]^2 &, 55, 0] (* Michael De Vlieger, Jun 02 2024 *)

Prog

(PARI) a(n) = my(T=(n^4+n^2)/2); T-sqrtint(T)^2
(Python)
from sympy import integer_nthroot
def A373330(n): return (T:=(n**4 + n**2) // 2)-(integer_nthroot(T, 2)[0])**2
# Karl-Heinz Hofmann, Jul 01 2024

Crossrefs

Cf. A000217, A000290, A002315, A037270, A061288, A373329, A373333.

A373331 and A373332 are the coordinates of the observed lower envelope of this sequence.

Sequence in context: A166654 A348318 A370674 * A131224 A073920 A130119

Adjacent sequences: A373327 A373328 A373329 * A373331 A373332 A373333

Keyword

nonn,look

Author

Hugo Pfoertner, Jun 02 2024

Status

approved