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A158557 a(n) = 225*n^2 + 15. 2
15, 240, 915, 2040, 3615, 5640, 8115, 11040, 14415, 18240, 22515, 27240, 32415, 38040, 44115, 50640, 57615, 65040, 72915, 81240, 90015, 99240, 108915, 119040, 129615, 140640, 152115, 164040, 176415, 189240, 202515, 216240, 230415, 245040, 260115 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (30*n^2 + 1)^2 - (225*n^2 + 15)*(2*n)^2 = 1 can be written as A158558(n)^2 - a(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

FORMULA

G.f.: 15*(1 + 13*x + 16*x^2)/(1-x)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {15, 240, 915}, 50] (* Vincenzo Librandi, Feb 14 2012 *)

225*Range[0, 40]^2+15 (* Harvey P. Dale, Apr 06 2019 *)

PROG

(MAGMA) I:=[15, 240, 915]; [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=0, 22, print1(225*n^2 + 15", ")); \\ Vincenzo Librandi, Feb 14 2012

CROSSREFS

Cf. A005843, A158558.

Sequence in context: A071811 A157456 A097262 * A220821 A090411 A154806

Adjacent sequences:  A158554 A158555 A158556 * A158558 A158559 A158560

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

Comment rewritten, a(0) added by R. J. Mathar, Oct 16 2009

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)