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A125169 16n+15. 8
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 (list; graph; refs; listen; history; text; internal format)
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(0)=15, a(1)=31, a(n)=2*a(n-1)-a(n-2). - 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

Contribution by Vincenzo Librandi, Jan 04 2012: (Start)

(MAGMA) I:=[15, 31]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]];

(PARI) a(n) = 16*n + 15. (End)

CROSSREFS

Cf. A158058.

Sequence in context: A031467 A045063 A044076 * A044457 A249452 A132757

Adjacent sequences:  A125166 A125167 A125168 * A125170 A125171 A125172

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Nov 22 2006

STATUS

approved

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Last modified April 30 22:27 EDT 2017. Contains 285686 sequences.