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

0,1

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

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*(4^2*t-2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A158058.

Sequence in context: A045063 A044076 A319282 * A044457 A249452 A132757

Adjacent sequences: A125166 A125167 A125168 * A125170 A125171 A125172

Keyword

nonn,easy

Author

Artur Jasinski, Nov 22 2006

Status

approved