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A195023
a(n) = 14*n^2 - 4*n.
10
0, 10, 48, 114, 208, 330, 480, 658, 864, 1098, 1360, 1650, 1968, 2314, 2688, 3090, 3520, 3978, 4464, 4978, 5520, 6090, 6688, 7314, 7968, 8650, 9360, 10098, 10864, 11658, 12480, 13330, 14208, 15114, 16048, 17010, 18000, 19018, 20064, 21138, 22240
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 10, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-axis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
FORMULA
a(n) = 2*A135703(n). - Bruno Berselli, Oct 13 2011
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 2*x*(5+9*x)/(1-x)^3. (End)
MATHEMATICA
Table[14n^2-4n, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 10, 48}, 50] (* Harvey P. Dale, Sep 05 2012 *)
PROG
(Magma) [14*n^2 - 4*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=14*n^2-4*n \\ Charles R Greathouse IV, Apr 10 2012
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 13 2011
EXTENSIONS
Corrected by Vincenzo Librandi, Oct 14 2011
STATUS
approved