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A158660 a(n) = 56*n^2 + 1. 2
1, 57, 225, 505, 897, 1401, 2017, 2745, 3585, 4537, 5601, 6777, 8065, 9465, 10977, 12601, 14337, 16185, 18145, 20217, 22401, 24697, 27105, 29625, 32257, 35001, 37857, 40825, 43905, 47097, 50401, 53817, 57345, 60985, 64737, 68601, 72577 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (56*n^2 + 1)^2 - (784*n^2 + 28)*(2*n)^2 = 1 can be written as a(n)^2 - A158659(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 + 54*x + 57*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 57, 225}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

56 Range[0, 40]^2+1 (* Harvey P. Dale, Jun 14 2022 *)

PROG

(MAGMA) I:=[1, 57, 225]; [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(56*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A158659, A005843.

Sequence in context: A338078 A336191 A277805 * A158668 A145296 A176635

Adjacent sequences:  A158657 A158658 A158659 * A158661 A158662 A158663

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 August 18 09:01 EDT 2022. Contains 356204 sequences. (Running on oeis4.)