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A053410 a(1) = 0, a(2) = 16, a(2n+1) = 10*a(2n) - a(2n-1), a(2n) = 10*a(2n-1) - a(2n-2) + 16.

%I A053410 #18 Jul 02 2025 16:01:59
%S A053410 0,16,160,1600,15840,156816,1552320,15366400,152111680,1505750416,
%T A053410 14905392480,147548174400,1460576351520,14458215340816,
%U A053410 143121577056640,1416757555225600,14024453975199360,138827782196768016
%N A053410 a(1) = 0, a(2) = 16, a(2n+1) = 10*a(2n) - a(2n-1), a(2n) = 10*a(2n-1) - a(2n-2) + 16.
%D A053410 O. Bottema: Verscheidenheden XXVI. Het vraagstuk van Malfatti, Euclides 25 (1949-50), pp. 144-149. [in Dutch].
%D A053410 O. Bottema, The Malfatti problem (translation of Het vraagstuk van Malfatti), Forum Geom. 1 (2001) 43-50.
%H A053410 G. C. Greubel, <a href="/A053410/b053410.txt">Table of n, a(n) for n = 1..1000</a>
%H A053410 <a href="http://forumgeom.fau.edu/FG2001volume1/FG200107index.html">Bottema article in Forum Geometricorum</a>
%H A053410 <a href="/malfatti.html">Bottema article, from Euclides</a>
%H A053410 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,0,-10,1).
%F A053410 a(n) = 10*a(n-1) - 10*a(n-3) + a(n-4).
%F A053410 G.f.: -16*x^2/((x-1)*(x+1)*(x^2-10*x+1)). - _Colin Barker_, Jun 24 2012
%t A053410 LinearRecurrence[{10,0,-10,1}, {0,16,160,1600}, 50] (* _G. C. Greubel_, May 25 2018 *)
%o A053410 (PARI) x='x+O('x^30); concat([0], Vec(-16*x^2/((x-1)*(x+1)*(x^2-10*x+1)))) \\ _G. C. Greubel_, May 25 2018
%o A053410 (Magma) I:=[0,16,160,1600]; [n le 4 select I[n] else 10*Self(n-1) - 10*Self(n-3) +Self(n-4): n in [1..30]]; // _G. C. Greubel_, May 25 2018
%Y A053410 Cf. A001078.
%K A053410 easy,nonn
%O A053410 1,2
%A A053410 Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Jan 09 2000
%E A053410 More terms from _James Sellers_, Jan 10 2000