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 A059403 #34 Dec 29 2024 21:01:11
%S A059403 0,0,0,1,4,9,20,36,64,100,156,225,324,441,600,784,1024,1296,1640,2025,
%T A059403 2500,3025,3660,4356,5184,6084,7140,8281,9604,11025,12656,14400,16384,
%U A059403 18496,20880,23409,26244,29241,32580,36100,40000,44100,48620,53361,58564,64009
%N A059403 Quarter-squared applied twice.
%H A059403 Harvey P. Dale, <a href="/A059403/b059403.txt">Table of n, a(n) for n = 0..1000</a> (first 501 terms from Harry J. Smith)
%H A059403 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 2, 0, -2, 4, -1, -2, 1).
%F A059403 a(n) = floor(floor(n^2/4)^2/4) = A002620(A002620(n)).
%F A059403 a(4*n) = 4n^4; a(4*n+1) = n^2*(2*n+1)^2;
%F A059403 a(4*n+2) = 2*n*(n+1)*(2*n*(n+1)+1); a(4*n+3) = (n+1)^2*(2*n+1)^2.
%F A059403 a(2n) = A060494(2n); a(2n-1) = A060494(2n-1)-A011861(n).
%F A059403 G.f.: x^3*(1 + 2*x + 2*x^3 + x^4)/((1 - x)^5*(1 + x)^3*(1 + x^2)). - _R. J. Mathar_, Sep 09 2008
%e A059403 a(9)=100 since the ninth quarter-square is 20 and the twentieth quarter-square is 100.
%t A059403 Floor[Floor[Range[0,50]^2/4]^2/4] (* or *) LinearRecurrence[{2,1,-4,2,0,-2,4,-1,-2,1},{0,0,0,1,4,9,20,36,64,100},50] (* _Harvey P. Dale_, Dec 13 2014 *)
%o A059403 (PARI) a(n) = { (n^2\4)^2\4 } \\ _Harry J. Smith_, Jun 26 2009
%Y A059403 Cf. A008233 for an alternative approach.
%K A059403 easy,nonn
%O A059403 0,5
%A A059403 _Henry Bottomley_, Mar 21 2001