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A158601 400n^2 + 20. 2
20, 420, 1620, 3620, 6420, 10020, 14420, 19620, 25620, 32420, 40020, 48420, 57620, 67620, 78420, 90020, 102420, 115620, 129620, 144420, 160020, 176420, 193620, 211620, 230420, 250020, 270420, 291620, 313620, 336420, 360020, 384420, 409620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (40*n^2+1)^2-(400*n^2+20)*(2*n)^2 = 1 can be written as A158602(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.: -20*(1+18*x+21*x^2)/(x-1)^3.

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

MATHEMATICA

400 Range[0, 40]^2+20  (* Harvey P. Dale, Feb 05 2011 *)

LinearRecurrence[{3, -3, 1}, {20, 420, 1620}, 50] (* Vincenzo Librandi, Feb 16 2012 *)

PROG

(MAGMA) I:=[20, 420, 1620]; [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 16 2012

(PARI) for(n=0, 40, print1(400*n^2 + 20", ")); \\ Vincenzo Librandi, Feb 16 2012

CROSSREFS

Cf. A005843, A158602.

Sequence in context: A196898 A068772 A230349 * A268738 A215290 A130832

Adjacent sequences:  A158598 A158599 A158600 * A158602 A158603 A158604

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 22 2009

EXTENSIONS

Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009

STATUS

approved

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Last modified February 25 13:30 EST 2018. Contains 299654 sequences. (Running on oeis4.)