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.

0, 16, 160, 1600, 15840, 156816, 1552320, 15366400, 152111680, 1505750416, 14905392480, 147548174400, 1460576351520, 14458215340816, 143121577056640, 1416757555225600, 14024453975199360, 138827782196768016

Offset: 1

Author

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Jan 09 2000

Keywords

• easy
• nonn

References

• O. Bottema: Verscheidenheden XXVI. Het vraagstuk van Malfatti, Euclides 25 (1949-50), pp. 144-149. [in Dutch].
• O. Bottema, The Malfatti problem (translation of Het vraagstuk van Malfatti), Forum Geom. 1 (2001) 43-50.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Bottema article in Forum Geometricorum
• Bottema article, from Euclides
• Index entries for linear recurrences with constant coefficients, signature (10,0,-10,1).

Crossrefs

Cf. A001078.

Programs

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

Mathematica

LinearRecurrence[{10,0,-10,1}, {0,16,160,1600}, 50] (* G. C. Greubel, May 25 2018 *)

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

Formula

a(n) = 10*a(n-1) - 10*a(n-3) + a(n-4).

G.f.: -16*x^2/((x-1)*(x+1)*(x^2-10*x+1)). - Colin Barker, Jun 24 2012

Extensions

More terms from James Sellers, Jan 10 2000