A368874 a(n) is the number of points with integer coordinates located strictly between the parabolas y = n - x^2 and y = x^2 - n.

1, 5, 11, 17, 25, 35, 45, 55, 65, 77, 91, 105, 119, 133, 147, 161, 177, 195, 213, 231, 249, 267, 285, 303, 321, 341, 363, 385, 407, 429, 451, 473, 495, 517, 539, 561, 585, 611, 637, 663, 689, 715, 741, 767, 793, 819, 845, 871, 897, 925, 955, 985, 1015, 1045, 1075, 1105, 1135, 1165, 1195

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Nicolay Avilov, Illustration for terms a(1)-a(6)

Formula

a(n) = 2*A095875(n-2) + A001650(n).

Example

For n=1, one point (0,0) lies between the parabolas y = 1 - x^2 and y = x^2 - 1, so that a(1) = 1.

Crossrefs

Cf. A001650, A095875.

Sequence in context: A314255 A369274 A246296 * A089110 A023489 A268307

Adjacent sequences: A368871 A368872 A368873 * A368875 A368876 A368877

Keyword

nonn

Author

Nicolay Avilov, Jan 08 2024

Status

approved