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 A075414 #13 Jul 29 2025 15:37:02 %S A075414 0,25,3025,308025,30858025,3086358025,308641358025,30864191358025, %T A075414 3086419691358025,308641974691358025,30864197524691358025, %U A075414 3086419753024691358025,308641975308024691358025,30864197530858024691358025,3086419753086358024691358025,308641975308641358024691358025 %N A075414 Squares of A002279: a(n) = (5*(10^n - 1)/9)^2. %C A075414 A transformation of the Wonderful Demlo numbers (A002477). %H A075414 Colin Barker, <a href="/A075414/b075414.txt">Table of n, a(n) for n = 0..100</a> %H A075414 Gérard Villemin, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/P100a500/Carrerep.htm">Variations sur les carrés</a>. %H A075414 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000). %F A075414 a(n) = A002279(n)^2 = (5*A002275(n))^2 = 25*A002275(n)^2. %F A075414 From _Colin Barker_, Jul 17 2019: (Start) %F A075414 G.f.: 25*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). %F A075414 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2. %F A075414 a(n) = 25*(10^n-1)^2/81. (End) %F A075414 From _Elmo R. Oliveira_, Jul 29 2025: (Start) %F A075414 E.g.f.: 25*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81. %F A075414 a(n) = 25*A002477(n). (End) %e A075414 a(2) = 55^2 = 3025. %o A075414 (PARI) concat(0, Vec(25*x*(1 + 10*x) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^20))) \\ _Colin Barker_, Jul 17 2019 %Y A075414 Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417. %Y A075414 Cf. A002275, A002279, A002283, A002477. %K A075414 easy,nonn %O A075414 0,2 %A A075414 Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002