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%I A102807 #41 Aug 01 2024 01:27:21
%S A102807 1,16,1156,111556,11115556,1111155556,111111555556,11111115555556,
%T A102807 1111111155555556,111111111555555556,11111111115555555556,
%U A102807 1111111111155555555556,111111111111555555555556,11111111111115555555555556,1111111111111155555555555556,111111111111111555555555555556
%N A102807 a(n) is the square of one plus the number consisting of n 3's.
%C A102807 Old name was: The number (333...334)^2.
%C A102807 An infinite sequence of squares with no zeros in base 10.
%C A102807 a(n) = A104265(2n) for n > 0. - _Chai Wah Wu_, Mar 24 2020
%D A102807 Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 31 at p. 61.
%D A102807 Italo Ghersi, Matematica dilettevole e curiosa, pp. 111-112, Hoepli, Milano, 1967. [_Vincenzo Librandi_, Dec 31 2008]
%H A102807 Seiichi Manyama, <a href="/A102807/b102807.txt">Table of n, a(n) for n = 0..500</a>
%H A102807 Emile Fourrey, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k875411n/f82.image">Récréations arithmétiques</a>, Vuibert, 1899 and after, Paris, pages 72-73.
%H A102807 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A102807 From _R. J. Mathar_, Jan 06 2009: (Start)
%F A102807 a(n) = (100^n + 4*10^n + 4)/9.
%F A102807 G.f.: (1 - 95*x + 490*x^2)/((1-x)*(100*x-1)*(10*x-1)). (End)
%F A102807 E.g.f.: exp(x)*(4 + 4*exp(9*x) + exp(99*x))/9. - _Stefano Spezia_, Jul 31 2024
%p A102807 a:= n-> (1+parse(cat(0, 3$n)))^2:
%p A102807 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 03 2018
%t A102807 Table[(10^n + 2)^2/9, {n, 0, 20}] (* _Paolo Xausa_, Jun 26 2024 *)
%Y A102807 Cf. A052041, A093137, A075415, A109344, A104265.
%K A102807 nonn,base,easy
%O A102807 0,2
%A A102807 _Ron Knott_, Feb 27 2005
%E A102807 New name from _Alois P. Heinz_, Sep 03 2018

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