This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A233149 #21 Aug 09 2025 12:02:29
%S A233149 -1,4,-24,13,-113,28,-316,49,-681,76,-1256,109,-2089,148,-3228,193,
%T A233149 -4721,244,-6616,301,-8961,364,-11804,433,-15193,508,-19176,589,
%U A233149 -23801,676,-29116,769,-35169,868,-42008,973,-49681,1084,-58236,1201,-67721,1324,-78184,1453,-89673,1588,-102236,1729,-115921,1876
%N A233149 a(n) = ((n^2+1)^3) - s, where s is the nearest square to (n^2+1)^3.
%H A233149 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%F A233149 a(n) = (n^2+1)^3 - (round(sqrt((n^2+1)^3)))^2.
%F A233149 Recurrence formula: a(n)= - a(n-2) + 4*a(n-4) - 6*a(n-6) + 4*a(n-8).
%F A233149 a(n) = -A077119(n^2+1). - _R. J. Mathar_, Jan 18 2021
%F A233149 a(2*n) = A056107(n). - _R. J. Mathar_, Jan 18 2021
%e A233149 Table of n, n^2, n^2+1, (n^2+1)^3, closest square, difference:
%e A233149 1 1 2 8 9 -1
%e A233149 2 4 5 125 121 4
%e A233149 3 9 10 1000 1024 -24
%e A233149 4 16 17 4913 4900 1
%e A233149 ...
%t A233149 aa = {}; Do[AppendTo[aa, (n^2 + 1)^3 - Round[Sqrt[(n^2 + 1)^3]]^2], {n, 1, 50}]; aa
%t A233149 LinearRecurrence[{0,4,0,-6,0,4,0,-1},{-1,4,-24,13,-113,28,-316,49},50] (* _Harvey P. Dale_, Aug 09 2025 *)
%Y A233149 Cf. A077119, A056107.
%K A233149 sign,easy
%O A233149 1,2
%A A233149 _Artur Jasinski_, Dec 05 2013