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Main axis of the square spiral whose edges have length A195013 and whose vertices are the numbers A195014.
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%I #28 Feb 09 2024 07:44:36

%S 0,2,12,24,44,66,96,128,168,210,260,312,372,434,504,576,656,738,828,

%T 920,1020,1122,1232,1344,1464,1586,1716,1848,1988,2130,2280,2432,2592,

%U 2754,2924,3096,3276,3458,3648,3840,4040,4242,4452,4664,4884

%N Main axis of the square spiral whose edges have length A195013 and whose vertices are the numbers A195014.

%C Sequence found by reading the line from 0, in the direction 0, 2, ..., and the same line from 0, in the direction 0, 12, ..., in the square spiral mentioned above. Axis perpendicular to A195016 in the same spiral.

%C Also four times A005475 and positives A152965 interleaved.

%H Vincenzo Librandi, <a href="/A195015/b195015.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F From _Bruno Berselli_, Oct 14 2011: (Start)

%F G.f.: 2*x*(1+4*x)/((1+x)*(1-x)^3).

%F a(n) = (2*n*(5*n+2) + 3*(-1)^n-3)/4.

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

%F a(n) + a(n-1) = A135706(n). (End)

%t LinearRecurrence[{2, 0, -2, 1}, {0, 2, 12, 24}, 50] (* _Paolo Xausa_, Feb 09 2024 *)

%o (Magma) [(2*n*(5*n+2)+3*(-1)^n-3)/4: n in [0..50]]; // _Vincenzo Librandi_, Oct 28 2011

%Y Cf. A000566, A005475, A005476, A028895, A033571, A152965, A153126, A195013, A195014, A195016.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Sep 26 2011