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A158672 a(n) = 900*n^2 + 30. 2
30, 930, 3630, 8130, 14430, 22530, 32430, 44130, 57630, 72930, 90030, 108930, 129630, 152130, 176430, 202530, 230430, 260130, 291630, 324930, 360030, 396930, 435630, 476130, 518430, 562530, 608430, 656130, 705630, 756930, 810030, 864930, 921630 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (60*n^2 + 1)^2 - (900*n^2 + 30)*(2*n)^2 = 1 can be written as A158673(n)^2 - a(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.: -30*(1 + 28*x + 31*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {30, 930, 3630}, 50] (* Vincenzo Librandi, Feb 19 2012 *)

PROG

MAGMA) I:=[30, 930, 3630]; [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 19 2012

(PARI) for(n=0, 40, print1(900*n^2 + 30", ")); \\ Vincenzo Librandi, Feb 19 2012

CROSSREFS

Cf. A005843, A158673.

Sequence in context: A042742 A144350 A111216 * A268948 A276396 A291070

Adjacent sequences:  A158669 A158670 A158671 * A158673 A158674 A158675

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 24 2009

EXTENSIONS

Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009

STATUS

approved

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Last modified June 24 21:09 EDT 2021. Contains 345425 sequences. (Running on oeis4.)