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A158540 a(n) = 22*n^2 - 1. 2
21, 87, 197, 351, 549, 791, 1077, 1407, 1781, 2199, 2661, 3167, 3717, 4311, 4949, 5631, 6357, 7127, 7941, 8799, 9701, 10647, 11637, 12671, 13749, 14871, 16037, 17247, 18501, 19799, 21141, 22527, 23957, 25431, 26949, 28511, 30117, 31767 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (22*n^2 - 1)^2 - (121*n^2 - 11)*(2*n)^2 = 1 can be written as a(n)^2 - A158539(n)*A005843(n)^2 = 1.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

FORMULA

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

G.f.: x*(-21 - 24*x + x^2)/(x-1)^3.

MATHEMATICA

22Range[40]^2-1 (* or *) LinearRecurrence[{3, -3, 1}, {21, 87, 197}, 40]

PROG

MAGMA) I:=[21, 87, 197]; [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 14 2012

(PARI) for(n=1, 40, print1(22*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 14 2012

CROSSREFS

Cf. A005843, A158539.

Sequence in context: A301540 A240518 A219850 * A304514 A219886 A211464

Adjacent sequences:  A158537 A158538 A158539 * A158541 A158542 A158543

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

Comment rewritten by R. J. Mathar, Oct 16 2009

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)