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Centered 36-gonal numbers.
7

%I #35 Feb 11 2022 04:49:37

%S 1,37,109,217,361,541,757,1009,1297,1621,1981,2377,2809,3277,3781,

%T 4321,4897,5509,6157,6841,7561,8317,9109,9937,10801,11701,12637,13609,

%U 14617,15661,16741,17857,19009,20197,21421,22681,23977,25309,26677,28081,29521

%N Centered 36-gonal numbers.

%C 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 Vincenzo Librandi, <a href="/A195316/b195316.txt">Table of n, a(n) for n = 1..10000</a>

%H John Elias, <a href="/A195316/a195316.png">Illustration of initial terms</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 18*n^2 - 18*n + 1.

%F G.f.: -x*(1 + 34*x + x^2) / (x-1)^3. - _R. J. Mathar_, Sep 18 2011

%F Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7)*Pi/6)/(6*sqrt(7)). - _Amiram Eldar_, Feb 11 2022

%t Table[18*n^2 - 18*n + 1, {n, 1, 40}] (* _Amiram Eldar_, Feb 11 2022 *)

%o (Magma) [(18*n^2-18*n+1): n in [1..50]]; // _Vincenzo Librandi_, Sep 19 2011

%o (PARI) a(n)=18*n^2-18*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Bisection of A195147.

%Y Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195317, A195318.

%K nonn,easy

%O 1,2

%A _Omar E. Pol_, Sep 16 2011