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 A295643 #38 Feb 06 2023 20:00:55
%S A295643 0,0,0,0,1,1,1,1,4,4,4,4,9,9,9,9,16,16,16,16,25,25,25,25,36,36,36,36,
%T A295643 49,49,49,49,64,64,64,64,81,81,81,81,100,100,100,100,121,121,121,121,
%U A295643 144,144,144,144,169,169,169,169,196,196,196,196,225,225,225
%N A295643 Squares repeated 4 times; a(n) = floor(n/4)^2.
%C A295643 a(n+1) is the sum of the smallest odd parts of the partitions of n into two distinct parts. For example, a(11) = 4; the partitions of 10 into two distinct parts are (9,1), (8,2), (7,3) and (6,4). The sum of the smallest odd parts in these partitions is then 1+3 = 4.
%C A295643 a(n+2) is the sum of the smallest odd parts of the partitions of n into two parts. For example, a(8) = 4; the partitions of 6 into two parts are (5,1), (4,2) and (3,3). The sum of the smallest odd parts is then 1+3 = 4.
%H A295643 Colin Barker, <a href="/A295643/b295643.txt">Table of n, a(n) for n = 0..1000</a>
%H A295643 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A295643 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).
%F A295643 a(n) = A002265(n)^2.
%F A295643 a(2n) = a(2n+1) = floor(n/2)^2 = A004526(n)^2 = A008794(n).
%F A295643 a(4n) = A000290(n).
%F A295643 a(n) = Sum_{i=1..floor(n/2)-1} i * (i mod 2).
%F A295643 From _Colin Barker_, Nov 25 2017: (Start)
%F A295643 G.f.: x^4*(1 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)^2).
%F A295643 a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9) for n>8.
%F A295643 (End)
%F A295643 a(n) = (1/16)*(n-(3-(-1)^n-2*(-1)^((2*n-1+(-1)^n)/4))/2)^2. - _Iain Fox_, Dec 18 2017
%p A295643 A295643:=n->floor(n/4)^2: seq(A295643(n), n=0..100);
%t A295643 Floor[Range[0, 80]/4]^2
%o A295643 (Magma) [Floor(n/4)^2 : n in [0..100]];
%o A295643 (PARI) concat(vector(4), Vec(x^4*(1 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)^2) + O(x^100))) \\ _Colin Barker_, Nov 25 2017
%o A295643 (PARI) a(n) = (n\4)^2; \\ _Altug Alkan_, Dec 17 2017
%o A295643 (Python)
%o A295643 def A295643(n): return (n>>2)**2 # _Chai Wah Wu_, Feb 06 2023
%Y A295643 Cf. A000290, A002265, A004526, A008794.
%Y A295643 See also the quarter-squares, A002620.
%K A295643 nonn,easy
%O A295643 0,9
%A A295643 _Wesley Ivan Hurt_, Nov 25 2017