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A158563 a(n) = 32*n^2 - 1. 4
31, 127, 287, 511, 799, 1151, 1567, 2047, 2591, 3199, 3871, 4607, 5407, 6271, 7199, 8191, 9247, 10367, 11551, 12799, 14111, 15487, 16927, 18431, 19999, 21631, 23327, 25087, 26911, 28799, 30751, 32767, 34847, 36991, 39199, 41471, 43807, 46207 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (32*n^2-1)^2 - (256*n^2-16)*(2*n)^2 = 1 can be written as a(n)^2 - A158562(n)*A005843(n)^2 = 1. [comment rewritten by R. J. Mathar, Oct 16 2009]

From Omar E. Pol, Apr 21 2021: (Start)

Sequence found by reading the line from 31, in the direction 31, 127, ..., in the rectangular spiral whose vertices are the generalized 18-gonal numbers A274979.

The spiral begins as follows:

       46_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _18

        |                                                        |

        |                            0                           |

        |                            |_ _ _ _ _ _ _ _ _ _ _ _ _ _|

        |                            1                           15

        |

       51

(End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(-31-34*x+x^2)/(x-1)^3.

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

a(n) = A244082(n) - 1. - Omar E. Pol, Apr 21 2021

MATHEMATICA

32 Range[40]^2 - 1  (* Harvey P. Dale, Mar 04 2011 *)

CoefficientList[Series[(- 31 - 34 x + x^2) / (x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 11 2013 *)

PROG

(MAGMA) [32*n^2-1: n in [1..40]]; // Vincenzo Librandi, Sep 11 2013

(PARI) a(n)=32*n^2-1 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A005843, A010021, A158562, A158575, A244082.

Cf. A274979 (generalized 18-gonal numbers).

Sequence in context: A095322 A127578 A333245 * A079141 A049203 A065403

Adjacent sequences:  A158560 A158561 A158562 * A158564 A158565 A158566

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

STATUS

approved

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Last modified June 30 15:29 EDT 2022. Contains 354943 sequences. (Running on oeis4.)