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A195026 a(n) = 7*n*(2*n + 1).

%I A195026 #38 Dec 30 2024 04:28:32
%S A195026 0,21,70,147,252,385,546,735,952,1197,1470,1771,2100,2457,2842,3255,
%T A195026 3696,4165,4662,5187,5740,6321,6930,7567,8232,8925,9646,10395,11172,
%U A195026 11977,12810,13671,14560,15477,16422,17395,18396,19425,20482,21567,22680,23821,24990
%N A195026 a(n) = 7*n*(2*n + 1).
%C A195026 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 A195026 Sum of the numbers from 6*n to 8*n. - _Wesley Ivan Hurt_, Dec 23 2015
%H A195026 Vincenzo Librandi, <a href="/A195026/b195026.txt">Table of n, a(n) for n = 0..10000</a>
%H A195026 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195026 a(n) = 14*n^2 + 7*n.
%F A195026 a(n) = 7*A014105(n). - _Bruno Berselli_, Oct 13 2011
%F A195026 From _Colin Barker_, Apr 09 2012: (Start)
%F A195026 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F A195026 G.f.: 7*x*(3+x)/(1-x)^3. (End)
%F A195026 a(n) = Sum_{i=6*n..8*n} i. - _Wesley Ivan Hurt_, Dec 23 2015
%F A195026 E.g.f.: 7*exp(x)*x*(3 + 2*x). - _Elmo R. Oliveira_, Dec 29 2024
%p A195026 A195026:=n->7*n*(2*n+1): seq(A195026(n), n=0..50); # _Wesley Ivan Hurt_, Dec 23 2015
%t A195026 Table[7*n*(2*n + 1), {n, 0, 50}] (* _Wesley Ivan Hurt_, Dec 23 2015 *)
%t A195026 LinearRecurrence[{3,-3,1},{0,21,70},50] (* _Harvey P. Dale_, Apr 26 2017 *)
%o A195026 (Magma) [14*n^2 +7*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011
%o A195026 (PARI) a(n)=7*n*(2*n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195026 Cf. A014105, A144555, A152760, A195019, A195020, A195021, A195023, A195024, A195025, A195320.
%Y A195026 Cf. A185019, A193053, A198017.
%K A195026 nonn,easy
%O A195026 0,2
%A A195026 _Omar E. Pol_, Oct 13 2011