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 A010762 #79 Jun 01 2025 16:42:47
%S A010762 0,0,1,2,2,6,6,8,12,15,15,24,24,28,35,40,40,54,54,60,70,77,77,96,96,
%T A010762 104,117,126,126,150,150,160,176,187,187,216,216,228,247,260,260,294,
%U A010762 294,308,330,345,345,384,384,400,425,442,442,486,486,504,532,551
%N A010762 a(n) = floor(n/2) * floor(n/3).
%C A010762 a(n) is also the number of 5 boxes polyomino (invert U patterns) packing into n X n square. The 6 boxes 2 X 3 (rectangular patterns) also gives the same sequence but difference in squares left. See illustration in links. - _Kival Ngaokrajang_, Nov 10 2013
%H A010762 Vincenzo Librandi, <a href="/A010762/b010762.txt">Table of n, a(n) for n = 1..1000</a>
%H A010762 Kival Ngaokrajang, <a href="/A010762/a010762_1.pdf">Illustration of initial terms of invert u and 2 X 3 rectangular patterns</a>.
%H A010762 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1,1,0,-1,-1,0,1).
%F A010762 a(n) = A004526(n) * A002264(n). - _Reinhard Zumkeller_, Jul 25 2005
%F A010762 a(n) = a(n-2) + a(n-3) - a(n-5) + a(n-6) - a(n-8) - a(n-9) + a(n-11). - _Clark Kimberling_, May 18 2012
%F A010762 G.f.: -x^3*(x^7+x^6+x^5+2*x^4+3*x^3+x^2+2*x+1) / ((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+x+1)^2). - _Colin Barker_, Apr 05 2013
%F A010762 Sum_{n>=3} (-1)^(n+1)/a(n) = sqrt(3)*Pi/4 + 9*log(3)/4 - 2*log(2) - 3/2. - _Amiram Eldar_, Mar 30 2023
%F A010762 E.g.f.: (3*(x - 1)*x*cosh(x) - sqrt(3)*exp(-x/2)*(1 + exp(x) + 4*x)*sin(sqrt(3)*x/2)/2 + 3*cos(sqrt(3)*x/2)*sinh(x/2) + 3*(1 + x^2)*sinh(x))/18. - _Stefano Spezia_, Jun 01 2025
%p A010762 [ seq(floor(n/2)*floor(n/3), n=1..64) ];
%t A010762 Table[Floor[n/2]*Floor[n/3], {n, 1, 70}] (* _Clark Kimberling_, May 18 2012 *)
%t A010762 CoefficientList[Series[- x^2 (x^7 + x^6 + x^5 + 2 x^4 + 3 x^3 + x^2 + 2 x+1)/((x - 1)^3 (x + 1)^2 (x^2 - x + 1) (x^2 + x + 1)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t A010762 LinearRecurrence[{0,1,1,0,-1,1,0,-1,-1,0,1},{0,0,1,2,2,6,6,8,12,15,15},60] (* _Harvey P. Dale_, Jan 09 2016 *)
%o A010762 (Magma) [Floor(n/2)*Floor(n/3) : n in [1..50]]; // _Wesley Ivan Hurt_, Jun 22 2014
%o A010762 (PARI) a(n) = (n\2) * (n\3) \\ _Charles R Greathouse IV_, Oct 07 2015; corrected by _Michel Marcus_, Jun 01 2025
%Y A010762 Cf. A002264, A004526, A010761, A110533, A242669.
%K A010762 nonn,easy
%O A010762 1,4
%A A010762 _N. J. A. Sloane_, _Simon Plouffe_