cp's OEIS Frontend

A075416 Squares of A002281.

%I A075416 #11 Jul 30 2025 00:58:08
%S A075416 0,49,5929,603729,60481729,6049261729,604937061729,60493815061729,
%T A075416 6049382595061729,604938270395061729,60493827148395061729,
%U A075416 6049382715928395061729,604938271603728395061729,60493827160481728395061729,6049382716049261728395061729,604938271604937061728395061729
%N A075416 Squares of A002281.
%C A075416 A transformation of the Wonderful Demlo numbers (A002477).
%H A075416 Colin Barker, <a href="/A075416/b075416.txt">Table of n, a(n) for n = 0..100</a>
%H A075416 Gérard Villemin, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/P100a500/Carrerep.htm">Variations sur les carrés</a>.
%H A075416 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A075416 a(n) = A002281(n)^2 = (7*A002275(n))^2 = 49*A002275(n)^2.
%F A075416 From _Colin Barker_, Jul 17 2019: (Start)
%F A075416 G.f.: 49*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F A075416 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
%F A075416 a(n) = 49*(10^n-1)^2/81. (End)
%F A075416 From _Elmo R. Oliveira_, Jul 29 2025: (Start)
%F A075416 E.g.f.: 49*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/81.
%F A075416 a(n) = 49*A002477(n). (End)
%e A075416 a(2) = 77^2 = 5929.
%o A075416 (PARI) concat(0, Vec(49*x*(1 + 10*x) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^20))) \\ _Colin Barker_, Jul 17 2019
%Y A075416 Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417.
%Y A075416 Cf. A002275, A002281, A002283, A002477.
%K A075416 easy,nonn
%O A075416 0,2
%A A075416 Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002