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A135453 a(n) = 12*n^2. 12
0, 12, 48, 108, 192, 300, 432, 588, 768, 972, 1200, 1452, 1728, 2028, 2352, 2700, 3072, 3468, 3888, 4332, 4800, 5292, 5808, 6348, 6912, 7500, 8112, 8748, 9408, 10092, 10800, 11532, 12288, 13068, 13872, 14700, 15552, 16428, 17328, 18252, 19200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Areas of perfect 4:3 rectangles (for n>0).

Sequence found by reading the line from 0, in the direction 0, 12,..., in the square spiral whose vertices are the generalized octagonal numbers A001082. Semi-axis opposite to A069190 in the same spiral. - Omar E. Pol, Sep 16 2011

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..10000

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

FORMULA

a(n) = A000290(n)*12 = A001105(n)*6 = A033428(n)*4 = A016742(n)*3 = A033581(n)*2. - Omar E. Pol, Dec 13 2008

a(n) = a(n-1)+24*n-12, n>0. - Vincenzo Librandi, Nov 24 2010

EXAMPLE

192 is on the list since 16*12 is a 4:3 rectangle with integer sides and an area of 192.

MATHEMATICA

Table[12*n^2, {n, 1, 60}] (* Stefan Steinerberger, Dec 17 2007 *)

PROG

(PARI) a(n)=12*n^2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Sequence in context: A213493 A009958 A256695 * A165280 A280058 A173548

Adjacent sequences:  A135450 A135451 A135452 * A135454 A135455 A135456

KEYWORD

nonn,easy

AUTHOR

Ben Paul Thurston, Dec 14 2007

EXTENSIONS

More terms from Stefan Steinerberger, Dec 17 2007

Minor edits from Omar E. Pol, Dec 15 2008

STATUS

approved

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Last modified August 19 14:06 EDT 2017. Contains 290808 sequences.