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%I #36 Sep 08 2022 08:45:59
%S 0,24,76,156,264,400,564,756,976,1224,1500,1804,2136,2496,2884,3300,
%T 3744,4216,4716,5244,5800,6384,6996,7636,8304,9000,9724,10476,11256,
%U 12064,12900,13764,14656,15576,16524,17500,18504,19536,20596,21684,22800
%N a(n) = 2*n*(7*n + 5).
%C Sequence found by reading the line from 0, in the direction 0, 24, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-axis opposite to A195023 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
%H Vincenzo Librandi, <a href="/A195027/b195027.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 14*n^2 + 10*n.
%F a(n) = 4*A179986(n). - _Bruno Berselli_, Oct 13 2011
%F G.f.: 4*x*(6+x)/(1-x)^3. - _Colin Barker_, Jan 09 2012
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=24, a(2)=76. - _Harvey P. Dale_, Jul 24 2012
%t Table[2n(7n+5),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,24,76},50] (* _Harvey P. Dale_, Jul 24 2012 *)
%o (Magma) [14*n^2 +10*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o (PARI) a(n)=2*n*(7*n+5) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A144555, A152760, A179986, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195320.
%Y Cf. A185019, A193053, A198017.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Oct 13 2011
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