cp's OEIS Frontend

A075413 Squares of A002278.

%I A075413 #11 Jul 29 2025 11:10:08
%S A075413 0,16,1936,197136,19749136,1975269136,197530469136,19753082469136,
%T A075413 1975308602469136,197530863802469136,19753086415802469136,
%U A075413 1975308641935802469136,197530864197135802469136,19753086419749135802469136,1975308641975269135802469136,197530864197530469135802469136
%N A075413 Squares of A002278.
%C A075413 A transformation of the Wonderful Demlo numbers (A002477).
%H A075413 Colin Barker, <a href="/A075413/b075413.txt">Table of n, a(n) for n = 0..100</a>
%H A075413 Gérard Villemin, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/P100a500/Carrerep.htm">Variations sur les carrés</a>.
%H A075413 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A075413 a(n) = A002278(n)^2 = (4*A002275(n))^2 = 16*A002275(n)^2.
%F A075413 From _Colin Barker_, Jul 17 2019: (Start)
%F A075413 G.f.: 16*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F A075413 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
%F A075413 a(n) = 16*(10^n-1)^2/81. (End)
%F A075413 From _Elmo R. Oliveira_, Jul 29 2025: (Start)
%F A075413 E.g.f.: 16*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81.
%F A075413 a(n) = 16*A002477(n). (End)
%e A075413 a(2) = 44^2 = 1936.
%o A075413 (PARI) concat(0, Vec(16*x*(1 + 10*x) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^20))) \\ _Colin Barker_, Jul 17 2019
%Y A075413 Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417.
%Y A075413 Cf. A002275, A002278, A002283, A002477.
%K A075413 easy,nonn
%O A075413 0,2
%A A075413 Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002