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A158646 a(n) = 54*n^2 + 1. 2
1, 55, 217, 487, 865, 1351, 1945, 2647, 3457, 4375, 5401, 6535, 7777, 9127, 10585, 12151, 13825, 15607, 17497, 19495, 21601, 23815, 26137, 28567, 31105, 33751, 36505, 39367, 42337, 45415, 48601, 51895, 55297, 58807, 62425, 66151, 69985 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (54*n^2 + 1)^2 - (729*n^2 + 27)*(2*n)^2 = 1 can be written as a(n)^2 - A158645(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

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

FORMULA

G.f.: -(1 + 52*x + 55*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 55, 217}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(MAGMA) I:=[1, 55, 217]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 17 2012

(PARI) for(n=0, 40, print1(54*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A005843, A158645.

Sequence in context: A161763 A189005 A105442 * A294461 A013550 A254148

Adjacent sequences:  A158643 A158644 A158645 * A158647 A158648 A158649

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 23 2009

EXTENSIONS

Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009

STATUS

approved

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Last modified February 25 11:34 EST 2020. Contains 332233 sequences. (Running on oeis4.)