cp's OEIS Frontend

A075412 Squares of A002277.

%I A075412 #38 Jul 30 2025 00:58:03
%S A075412 0,9,1089,110889,11108889,1111088889,111110888889,11111108888889,
%T A075412 1111111088888889,111111110888888889,11111111108888888889,
%U A075412 1111111111088888888889,111111111110888888888889,11111111111108888888888889,1111111111111088888888888889,111111111111110888888888888889
%N A075412 Squares of A002277.
%C A075412 A transformation of the Wonderful Demlo numbers (A002477).
%H A075412 Vincenzo Librandi, <a href="/A075412/b075412.txt">Table of n, a(n) for n = 0..200</a>
%H A075412 Gérard Villemin, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/P100a500/Carrerep.htm">Variations sur les carrés</a>.
%H A075412 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A075412 a(n) = A002277(n)^2 = (3*A002275(n))^2 = 9*A002275(n)^2.
%F A075412 a(n) = {111111... (2n times)} - 2*{ 111... (n times)} a(n) = A000042(2*n) - 2*A000042(n). - _Amarnath Murthy_, Jul 21 2003
%F A075412 a(n) = {333... (n times)}^2 = {111...(n times)}{000... (n times)} - {111... (n times)}. For example, 333^2 = 111000 - 111 = 110889. - _Kyle D. Balliet_, Mar 07 2009
%F A075412 From _Reinhard Zumkeller_, May 31 2010: (Start)
%F A075412 a(n) = A002283(n)*A002275(n).
%F A075412 For n>0, a(n) = (A002275(n-1)*10^n + A002282(n-1))*10 + 9. (End)
%F A075412 a(n) = (10^(n+1)-10)^2/900. - _José de Jesús Camacho Medina_, Apr 01 2016
%F A075412 From _Elmo R. Oliveira_, Jul 27 2025: (Start)
%F A075412 G.f.: 9*x*(1+10*x)/((1-x)*(1-10*x)*(1-100*x)).
%F A075412 E.g.f.: exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9.
%F A075412 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3).
%F A075412 a(n) = 9*A002477(n). (End)
%e A075412 a(2) = 33^2 = 1089.
%e A075412 Contribution from _Reinhard Zumkeller_, May 31 2010: (Start)
%e A075412 n=1: ...................... 9 = 9 * 1;
%e A075412 n=2: ................... 1089 = 99 * 11;
%e A075412 n=3: ................. 110889 = 999 * 111;
%e A075412 n=4: ............... 11108889 = 9999 * 1111;
%e A075412 n=5: ............. 1111088889 = 99999 * 11111;
%e A075412 n=6: ........... 111110888889 = 999999 * 111111;
%e A075412 n=7: ......... 11111108888889 = 9999999 * 1111111;
%e A075412 n=8: ....... 1111111088888889 = 99999999 * 11111111;
%e A075412 n=9: ..... 111111110888888889 = 999999999 * 111111111. (End)
%t A075412 LinearRecurrence[{11, -10}, {0, 3}, 20]^2 (* _Vincenzo Librandi_, Mar 20 2014 *)
%t A075412 Table[FromDigits[PadRight[{},n,9]]FromDigits[PadRight[{},n,1]],{n,0,15}] (* _Harvey P. Dale_, Feb 12 2023 *)
%Y A075412 Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417, A002283, A178630, A178631, A178632, A178633, A178634, A178635.
%Y A075412 Cf. A000042, A002277, A002275, A002282, A002283, A002477, A059988.
%K A075412 nonn,easy
%O A075412 0,2
%A A075412 Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002