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 A008217 #32 Aug 18 2025 12:18:36
%S A008217 0,0,0,0,1,1,1,2,4,4,4,6,9,9,9,12,16,16,16,20,25,25,25,30,36,36,36,42,
%T A008217 49,49,49,56,64,64,64,72,81,81,81,90,100,100,100,110,121,121,121,132,
%U A008217 144,144,144,156,169,169,169,182,196,196,196,210,225,225,225,240,256,256,256,272,289,289,289,306
%N A008217 a(n) = floor(n/4)*floor((n+1)/4).
%C A008217 Oblong numbers, squares and quarter-squares are subsequences: a(A004767(n)) = A002378(n); a(A008586(n)) = A000290(n); a(A005408(n)) = A002620(n). - _Reinhard Zumkeller_, Oct 09 2011
%H A008217 Reinhard Zumkeller, <a href="/A008217/b008217.txt">Table of n, a(n) for n = 0..10000</a>
%H A008217 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,0,-2,2,-2,1).
%F A008217 G.f.: -x^4*(x^2-x+1) / ((x-1)^3*(x+1)*(x^2+1)^2). - _Colin Barker_, Mar 31 2013
%F A008217 From _Amiram Eldar_, May 10 2025: (Start)
%F A008217 Sum_{n>=4} 1/a(n) = Pi^2/2 + 1.
%F A008217 Sum_{n>=4} (-1)^n/a(n) = Pi^2/6 - 1. (End)
%t A008217 a[n_] := Floor[n/4] * Floor[(n+1)/4]; Array[a, 100, 0] (* _Amiram Eldar_, May 10 2025 *)
%t A008217 LinearRecurrence[{2,-2,2,0,-2,2,-2,1},{0,0,0,0,1,1,1,2},80] (* _Harvey P. Dale_, Aug 18 2025 *)
%o A008217 (Haskell)
%o A008217 a008217 n = a008217_list !! n
%o A008217 a008217_list = zipWith (*) (tail qs) qs where qs = map (`div` 4) [0..]
%o A008217 -- _Reinhard Zumkeller_, Oct 09 2011
%o A008217 (PARI) a(n) = floor(n/4)*floor((n+1)/4); /* _Joerg Arndt_, Mar 31 2013 */
%o A008217 (Python)
%o A008217 def A008217(n): return (n>>2)*(n+1>>2) # _Chai Wah Wu_, Feb 02 2023
%Y A008217 Cf. A000290, A002378, A002620, A004767, A005408, A008133, A008586.
%K A008217 nonn,easy
%O A008217 0,8
%A A008217 _N. J. A. Sloane_