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A158667 841*n^2 - 29. 2
812, 3335, 7540, 13427, 20996, 30247, 41180, 53795, 68092, 84071, 101732, 121075, 142100, 164807, 189196, 215267, 243020, 272455, 303572, 336371, 370852, 407015, 444860, 484387, 525596, 568487, 613060, 659315, 707252, 756871, 808172, 861155 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (58*n^2-1)^2-(841*n^2-29)*(2*n)^2 = 1 can be written as A158668(n)^2-a(n)*A005843(n)^2 =1.

LINKS

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

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

FORMULA

G.f.: 29*x*(-28-31*x+x^2)/(x-1)^3.

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

MAPLE

A158667:=n->841*n^2 - 29; seq(A158667(k), k=1..50); # Wesley Ivan Hurt, Nov 01 2013

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {812, 3335, 7540}, 40] (* or *) 29 (29 Range[40]^2 - 1) (* Harvey P. Dale, Oct 31 2011 *)

PROG

(MAGMA) I:=[812, 3335, 7540]; [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 18 2012

(PARI) for(n=1, 40, print1(841*n^2-29", ")); \\ Vincenzo Librandi, Feb 18 2012

CROSSREFS

Cf. A005843, A158668.

Sequence in context: A093633 A045228 A252223 * A035854 A099116 A183820

Adjacent sequences:  A158664 A158665 A158666 * A158668 A158669 A158670

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 24 2009

EXTENSIONS

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

STATUS

approved

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Last modified August 16 05:55 EDT 2022. Contains 356160 sequences. (Running on oeis4.)