

A135453


a(n) = 12*n^2.


17



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. Semiaxis opposite to A069190 in the same spiral.  Omar E. Pol, Sep 16 2011
For n>2, a(n) is the fifth least number k = x + y, with x>0 and y>0, such that there are n different pairs (x,y) for which x*y/k is an integer.  Paolo P. Lava, Jan 29 2018


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(n1)+24*n12, 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.


MAPLE

seq(12*h^2, n=0..100); # Muniru A Asiru, Jan 29 2018


MATHEMATICA

Table[12*n^2, {n, 1, 60}] (* Stefan Steinerberger, Dec 17 2007 *)
LinearRecurrence[{3, 3, 1}, {0, 12, 48}, 50] (* Harvey P. Dale, Jan 19 2020 *)


PROG

(PARI) a(n)=12*n^2 \\ Charles R Greathouse IV, Jun 17 2017
(GAP) List([0..100], n>12*n^2); # Muniru A Asiru, Jan 29 2018


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



