cp's OEIS Frontend

A195316 Centered 36-gonal numbers.

%I A195316 #39 Nov 15 2024 09:05:55
%S A195316 1,37,109,217,361,541,757,1009,1297,1621,1981,2377,2809,3277,3781,
%T A195316 4321,4897,5509,6157,6841,7561,8317,9109,9937,10801,11701,12637,13609,
%U A195316 14617,15661,16741,17857,19009,20197,21421,22681,23977,25309,26677,28081,29521,30997,32509
%N A195316 Centered 36-gonal numbers.
%C A195316 Sequence found by reading the line from 1, in the direction 1, 37, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Semi-axis opposite to A195321 in the same spiral.
%H A195316 Vincenzo Librandi, <a href="/A195316/b195316.txt">Table of n, a(n) for n = 1..10000</a>
%H A195316 John Elias, <a href="/A195316/a195316.png">Illustration of initial terms</a>.
%H A195316 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195316 a(n) = 18*n^2 - 18*n + 1.
%F A195316 G.f.: -x*(1 + 34*x + x^2)/(x-1)^3. - _R. J. Mathar_, Sep 18 2011
%F A195316 Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7)*Pi/6)/(6*sqrt(7)). - _Amiram Eldar_, Feb 11 2022
%F A195316 From _Elmo R. Oliveira_, Nov 14 2024: (Start)
%F A195316 E.g.f.: exp(x)*(18*x^2 + 1) - 1.
%F A195316 a(n) = 2*A069131(n) - 1.
%F A195316 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A195316 Table[18*n^2 - 18*n + 1, {n, 1, 40}] (* _Amiram Eldar_, Feb 11 2022 *)
%o A195316 (Magma) [(18*n^2-18*n+1): n in [1..50]]; // _Vincenzo Librandi_, Sep 19 2011
%o A195316 (PARI) a(n)=18*n^2-18*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195316 Bisection of A195147.
%Y A195316 Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195317, A195318.
%Y A195316 Cf. A069131, A195160, A195321.
%K A195316 nonn,easy
%O A195316 1,2
%A A195316 _Omar E. Pol_, Sep 16 2011