A158127 a(n) = 100*n^2 + 2*n.

102, 404, 906, 1608, 2510, 3612, 4914, 6416, 8118, 10020, 12122, 14424, 16926, 19628, 22530, 25632, 28934, 32436, 36138, 40040, 44142, 48444, 52946, 57648, 62550, 67652, 72954, 78456, 84158, 90060, 96162, 102464, 108966, 115668, 122570

Offset: 1

Author

Vincenzo Librandi, Mar 13 2009

Keywords

• nonn
• easy

Comments

The identity (100*n + 1)^2 - (100*n^2 + 2*n)*10^2 = 1 can be written as A158128(n)^2 - a(n)*10^2 = 1. - Vincenzo Librandi, Feb 11 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(10^2*t+2)).
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A158128.

Programs

Magma

I:=[102, 404, 906]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012

Mathematica

Table[100n^2 +2n,{n,45}]  (* Harvey P. Dale, Mar 15 2011 *)
LinearRecurrence[{3, -3, 1}, {102, 404, 906}, 50] (* Vincenzo Librandi, Feb 11 2012 *)

PARI

for(n=1, 50, print1(100*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 11 2012

Formula

G.f.: x*(102 + 98*x)/(1-x)^3. - Vincenzo Librandi, Feb 11 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 11 2012