A125169 a(n) = 16*n + 15.

15, 31, 47, 63, 79, 95, 111, 127, 143, 159, 175, 191, 207, 223, 239, 255, 271, 287, 303, 319, 335, 351, 367, 383, 399, 415, 431, 447, 463, 479, 495, 511, 527, 543, 559, 575, 591, 607, 623, 639, 655, 671, 687, 703, 719, 735, 751, 767, 783, 799, 815, 831, 847

Offset: 0

Author

Artur Jasinski, Nov 22 2006

Keywords

• nonn
• easy

Comments

The identity (16*n + 15)^2 - (16*(n+1)^2 - 2*(n+1))*4^2 = 1 can be written as a(n)^2 - A158058(n+1)*4^2 = 1. - Vincenzo Librandi, Feb 01 2012

a(n-3), n >= 3, appears in the third column of triangle A239126 related to the Collatz problem. - Wolfdieter Lang, Mar 14 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, Recursive Sequences.
• Edward 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*(4^2*t-2)).
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A004771, A158058, A239126.

Programs

Magma

I:=[15, 31]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // Vincenzo Librandi, Jan 04 2012

Mathematica

Table[16n + 15, {n, 0, 100}]
LinearRecurrence[{2,-1},{15,31},100] (* or *) Range[15,1620,16] (* Harvey P. Dale, Jan 03 2012 *)

PARI

a(n) = 16*n + 15 \\ Vincenzo Librandi, Jan 04 2012

Formula

a(n) = 2*a(n-1) - a(n-2); a(0)=15, a(1)=31. - Harvey P. Dale, Jan 03 2012

O.g.f.: (15 + x)/(1 - x)^2. - Wolfdieter Lang, Mar 14 2014

From Elmo R. Oliveira, Apr 04 2025: (Start)

E.g.f.: exp(x)*(15 + 16*x).

a(n) = A004771(2*n+1). (End)