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A157337 a(n) = 128*n^2 + 32*n + 1. 2
161, 577, 1249, 2177, 3361, 4801, 6497, 8449, 10657, 13121, 15841, 18817, 22049, 25537, 29281, 33281, 37537, 42049, 46817, 51841, 57121, 62657, 68449, 74497, 80801, 87361, 94177, 101249, 108577, 116161, 124001, 132097, 140449, 149057 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (128*n^2+32*n+1)^2 - (4*n^2+n)*(64*n+8)^2 = 1 can be written as a(n)^2 - A007742(n)*A157336(n)^2 = 1 (see also second part of the comment in A157336). - Vincenzo Librandi, Jan 29 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

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

FORMULA

G.f.: x*(x^2 + 94*x + 161)/(1-x)^3. - Vincenzo Librandi, Jan 29 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 29 2012

a(n) = 2*A017077(n)^2 - 1. - Bruno Berselli, Jan 29 2012

E.g.f.: (1 + 160*x + 128*x^2)*exp(x) - 1. - G. C. Greubel, Feb 01 2018

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {161, 577, 1249}, 50] (* Vincenzo Librandi, Jan 29 2012 *)

PROG

(MAGMA) I:=[161, 577, 1249]; [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, Jan 29 2012

(PARI) for(n=1, 40, print1(128*n^2 + 32*n + 1", ")); \\ Vincenzo Librandi, Jan 29 2012

CROSSREFS

Cf. A007742, A157336.

Sequence in context: A209282 A157954 A159545 * A200869 A200883 A196635

Adjacent sequences:  A157334 A157335 A157336 * A157338 A157339 A157340

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 27 2009

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)