%I #21 Dec 15 2024 12:58:34
%S 0,13,78,195,364,585,858,1183,1560,1989,2470,3003,3588,4225,4914,5655,
%T 6448,7293,8190,9139,10140,11193,12298,13455,14664,15925,17238,18603,
%U 20020,21489,23010,24583,26208,27885,29614,31395,33228,35113,37050,39039,41080,43173
%N 13 times hexagonal numbers: a(n) = 13*n*(2*n-1).
%C Sequence found by reading the line from 0, in the direction 0, 13, ..., in the square spiral whose vertices are the generalized 15-gonal numbers.
%H Vincenzo Librandi, <a href="/A194713/b194713.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) = 26*n^2 - 13*n = 13*A000384(n).
%F a(n) = a(n-1) + 52*n - 39, a(0)=0. - _Vincenzo Librandi_, Oct 03 2011
%F From _Elmo R. Oliveira_, Dec 15 2024: (Start)
%F G.f.: 13*x*(1 + 3*x)/(1 - x)^3.
%F E.g.f.: 13*x*(1 + 2*x)*exp(x).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
%o (Magma) [13*n*(2*n-1): n in [0..50]]; // _Vincenzo Librandi_, Oct 03 2011
%o (PARI) a(n)=13*n*(2*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000384, A002939, A094159, A143698, A152745, A154617, A195320.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Oct 02 2011