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A158058 16n^2 - 2n. 2
14, 60, 138, 248, 390, 564, 770, 1008, 1278, 1580, 1914, 2280, 2678, 3108, 3570, 4064, 4590, 5148, 5738, 6360, 7014, 7700, 8418, 9168, 9950, 10764, 11610, 12488, 13398, 14340, 15314, 16320, 17358, 18428, 19530, 20664, 21830, 23028, 24258, 25520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (16*(n-1)+15)^2-(16*n^2-2*n)*4^2=1 can be written as A125169(n-1)^2-a(n)*4^2=1. - Vincenzo Librandi, Feb 01 2012

Sequence found by reading the line from 14, in the direction 14, 60,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012

LINKS

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(4^2*t-2)).

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

FORMULA

G.f.: x*(-14-18*x)/(x-1)^3.

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

MAPLE

seq(16*n^2-2*n, n=1..40); # Nathaniel Johnston, Jun 26 2011

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {14, 60, 138}, 40]

PROG

(MAGMA) [16*n^2-2*n: n in [1..40]]

(PARI) a(n) = 16*n^2-2*n.

CROSSREFS

Cf. A125169.

Sequence in context: A120371 A062022 A261282 * A100171 A063492 A051799

Adjacent sequences:  A158055 A158056 A158057 * A158059 A158060 A158061

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 12 2009

STATUS

approved

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Last modified August 28 15:16 EDT 2015. Contains 261125 sequences.