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%I #34 Sep 08 2022 08:45:59
%S 0,21,70,147,252,385,546,735,952,1197,1470,1771,2100,2457,2842,3255,
%T 3696,4165,4662,5187,5740,6321,6930,7567,8232,8925,9646,10395,11172,
%U 11977,12810,13671,14560,15477,16422,17395,18396,19425,20482,21567,22680,23821,24990
%N a(n) = 7*n*(2*n + 1).
%C Sequence found by reading the line from 0, in the direction 0, 21,..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-diagonal opposite to A195320 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
%C Sum of the numbers from 6n to 8n. - _Wesley Ivan Hurt_, Dec 23 2015
%H Vincenzo Librandi, <a href="/A195026/b195026.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 + 7*n.
%F a(n) = 7*A014105(n). - _Bruno Berselli_, Oct 13 2011
%F From _Colin Barker_, Apr 09 2012: (Start)
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
%F G.f.: 7*x*(3+x)/(1-x)^3. (End)
%F a(n) = Sum_{i=6n..8n} i. - _Wesley Ivan Hurt_, Dec 23 2015
%p A195026:=n->7*n*(2*n+1): seq(A195026(n), n=0..50); # _Wesley Ivan Hurt_, Dec 23 2015
%t Table[7*n*(2*n + 1), {n, 0, 50}] (* _Wesley Ivan Hurt_, Dec 23 2015 *)
%t LinearRecurrence[{3,-3,1},{0,21,70},50] (* _Harvey P. Dale_, Apr 26 2017 *)
%o (Magma) [14*n^2 +7*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o (PARI) a(n)=7*n*(2*n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A014105, A144555, A152760, A195019, A195020, A195021, A195023, A195024, A195025, A195320.
%Y Cf. A185019, A193053, A198017.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Oct 13 2011
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