A233149 a(n) = ((n^2+1)^3) - s, where s is the nearest square to (n^2+1)^3.

-1, 4, -24, 13, -113, 28, -316, 49, -681, 76, -1256, 109, -2089, 148, -3228, 193, -4721, 244, -6616, 301, -8961, 364, -11804, 433, -15193, 508, -19176, 589, -23801, 676, -29116, 769, -35169, 868, -42008, 973, -49681, 1084, -58236, 1201, -67721, 1324, -78184, 1453, -89673, 1588, -102236, 1729, -115921, 1876

Offset: 1

Author

Artur Jasinski, Dec 05 2013

Keywords

• sign
• easy

Examples

			Table of n, n^2, n^2+1, (n^2+1)^3, closest square, difference:
  1 1 2 8 9 -1
  2 4 5 125 121 4
  3 9 10 1000 1024 -24
  4 16 17 4913 4900 1
  ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A077119, A056107.

Programs

Mathematica

aa = {}; Do[AppendTo[aa, (n^2 + 1)^3 - Round[Sqrt[(n^2 + 1)^3]]^2], {n, 1, 50}]; aa
LinearRecurrence[{0,4,0,-6,0,4,0,-1},{-1,4,-24,13,-113,28,-316,49},50] (* Harvey P. Dale, Aug 09 2025 *)

Formula

a(n) = (n^2+1)^3 - (round(sqrt((n^2+1)^3)))^2.

Recurrence formula: a(n)= - a(n-2) + 4*a(n-4) - 6*a(n-6) + 4*a(n-8).

a(n) = -A077119(n^2+1). - R. J. Mathar, Jan 18 2021

a(2*n) = A056107(n). - R. J. Mathar, Jan 18 2021