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 A162675 #13 Jul 22 2025 06:56:11 %S A162675 0,0,114,2910,26490,145110,582540,1891764,5263020,13010580,29297070, %T A162675 61162530,119933814,223098330,396734520,678599880,1121985720, %U A162675 1800456264,2813598090,4293914310,6415006290,9401194110,13538735364,19188810300 %N A162675 Number of different fixed (possibly) disconnected pentominoes bounded (not necessarily tightly) by an n*n square. %C A162675 Fixed quasi-pentominoes. %H A162675 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1). %F A162675 a(n) = n*(n-1)*(n-2)*(n+1)*(5*n^4-10*n^3-7*n^2+12*n+6)/24. %F A162675 G.f.: x^3*(114+1884*x+4404*x^2+1884*x^3+114*x^4)/(1-x)^9. [_Colin Barker_, Apr 25 2012] %e A162675 a(3)=114: there are 114 rotations of the 21 free (possibly) disconnected pentominoes bounded (not necessarily tightly) by an 3*3 square; these include the F, P, T, U, V, W, X and Z (connected) pentominoes and 13 strictly disconnected pentominoes. %Y A162675 Cf. A162674, A162676, A162677, A094172 (free quasi-pentominoes). %K A162675 nonn,easy %O A162675 1,3 %A A162675 _David Bevan_, Jul 27 2009 %E A162675 Example moved to correct section, and ref to free quasi-pentominoes added by _David Bevan_, Mar 05 2011