cp's OEIS Frontend

A075415 Squares of A002280 or numbers (666...6)^2.

%I A075415 #38 Aug 01 2025 11:09:10
%S A075415 0,36,4356,443556,44435556,4444355556,444443555556,44444435555556,
%T A075415 4444444355555556,444444443555555556,44444444435555555556,
%U A075415 4444444444355555555556,444444444443555555555556,44444444444435555555555556,4444444444444355555555555556,444444444444443555555555555556
%N A075415 Squares of A002280 or numbers (666...6)^2.
%C A075415 A transformation of the Wonderful Demlo numbers (A002477).
%H A075415 Seiichi Manyama, <a href="/A075415/b075415.txt">Table of n, a(n) for n = 0..500</a>
%H A075415 Gérard Villemin, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/P100a500/Carrerep.htm">Variations sur les carrés</a>.
%H A075415 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A075415 a(n) = A002280(n)^2 = (6*A002275(n))^2 = 36*A002275(n)^2.
%F A075415 a(n) = (6*(10^n-1)/9)^2 = (4/9)*(10^(2*n) - 2*10^n + 1), which is n-1 4's, followed by a 3, n-1 5's and a 6. - _Ignacio Larrosa Cañestro_, Feb 26 2005
%F A075415 From _Reinhard Zumkeller_, May 31 2010: (Start)
%F A075415 a(n) = ((A002278(n-1)*10 + 3)*10^(n-1) + A002279(n-1))*10 + 6 for n>0.
%F A075415 a(n) = A002283(n)*A002278(n). (End)
%F A075415 G.f.: 36*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - _Arkadiusz Wesolowski_, Dec 26 2011
%F A075415 From _Elmo R. Oliveira_, Jul 27 2025: (Start)
%F A075415 E.g.f.: 4*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9.
%F A075415 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3).
%F A075415 a(n) = 36*A002477(n). (End)
%e A075415 a(2) = 66^2 = 4356.
%e A075415 From _Reinhard Zumkeller_, May 31 2010: (Start)
%e A075415 n=1: ..................... 36 = 9 * 4;
%e A075415 n=2: ................... 4356 = 99 * 44;
%e A075415 n=3: ................. 443556 = 999 * 444;
%e A075415 n=4: ............... 44435556 = 9999 * 4444;
%e A075415 n=5: ............. 4444355556 = 99999 * 44444;
%e A075415 n=6: ........... 444443555556 = 999999 * 444444;
%e A075415 n=7: ......... 44444435555556 = 9999999 * 4444444;
%e A075415 n=8: ....... 4444444355555556 = 99999999 * 44444444;
%e A075415 n=9: ..... 444444443555555556 = 999999999 * 444444444. (End)
%t A075415 Table[FromDigits[PadRight[{},n,6]]^2,{n,0,20}] (* or *) LinearRecurrence[ {111,-1110,1000},{0,36,4356},20] (* _Harvey P. Dale_, May 20 2021 *)
%Y A075415 Cf. A075411, A075412, A075413, A075414, A075415, A075416, A075417.
%Y A075415 Cf. A059988, A178630, A178631, A178632, A178633, A178634, A178635. [From _Reinhard Zumkeller_, May 31 2010]
%Y A075415 Cf. A002275, A002278, A002279,  A002280, A002283, A002477, A052041, A102807, A309827.
%K A075415 nonn,easy
%O A075415 0,2
%A A075415 Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002
%E A075415 Edited by _Alois P. Heinz_, Aug 21 2019 (merged with A102794, submitted by Richard C. Schroeppel, Feb 26 2005)