This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108211 #62 Jun 06 2025 11:14:45
%S A108211 17,65,145,257,401,577,785,1025,1297,1601,1937,2305,2705,3137,3601,
%T A108211 4097,4625,5185,5777,6401,7057,7745,8465,9217,10001,10817,11665,12545,
%U A108211 13457,14401,15377,16385,17425,18497,19601,20737,21905,23105,24337,25601,26897,28225,29585
%N A108211 a(n) = 16*n^2 + 1.
%C A108211 Area of a Maltese cross conventionally inscribed in a 5n X 5n-grid.
%C A108211 Areas of some other crosses, each made from unit squares, as shown in Weisstein's illustrations: Greek Cross = x-pentomino = 5. Latin Cross = 6. Saint Andrew's cross = crux decussata = 9. Saint Anthony's Cross = tau cross = crux commissa = 10. Gaullist Cross = cross of Lorraine or patriarchal cross = 13. Papal Cross = 22. - _Jonathan Vos Post_, Jun 18 2005
%C A108211 The identity (16*n^2 + 1)^2 - (64*n^2 + 8)*(2*n)^2 = 1 can be written as a(n)^2 - A158488(n)*A005843(n)^2 = 1. - _Vincenzo Librandi_, Feb 08 2012
%C A108211 Sequence found by reading the line from 17, in the direction 17, 65, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 02 2012
%C A108211 Conjecture: a(n) = floor(1/(1/(4*n) - log(2) + 1/(n+1) + 1/(n+2) + ... + 1/(2*n))). - _Clark Kimberling_, Sep 09 2014
%H A108211 Vincenzo Librandi, <a href="/A108211/b108211.txt">Table of n, a(n) for n = 1..10000</a>
%H A108211 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MalteseCross.html">Maltese Cross</a>.
%H A108211 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GaullistCross.html">Gaullist Cross</a>.
%H A108211 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreekCross.html">Greek Cross</a>.
%H A108211 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LatinCross.html">Latin Cross</a>.
%H A108211 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A108211 a(n) = A002522(4*n) = A016802(n) + 1.
%F A108211 G.f.: x*(17+14*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 08 2012
%F A108211 From _Amiram Eldar_, Jul 13 2020: (Start)
%F A108211 Sum_{n>=1} 1/a(n) = Pi*coth(Pi/4)/8 - 1/2.
%F A108211 Sum_{n>=1} (-1)^(n+1)/a(n) = 1/2 - Pi*csch(Pi/4)/8. (End)
%F A108211 From _Amiram Eldar_, Feb 05 2021: (Start)
%F A108211 Product_{n>=0} (1 + 1/a(n)) = sqrt(2)*csch(Pi/4)*sinh(Pi/sqrt(8)).
%F A108211 Product_{n>=1} (1 - 1/a(n)) = (Pi/4)*csch(Pi/4). (End)
%F A108211 From _Elmo R. Oliveira_, Jan 17 2025: (Start)
%F A108211 E.g.f.: exp(x)*(16*x^2 + 16*x + 1) - 1.
%F A108211 a(n) = A053755(2*n).
%F A108211 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%p A108211 A108211:=n->16*n^2+1: seq(A108211(n), n=1..50); # _Wesley Ivan Hurt_, Sep 24 2014
%t A108211 LinearRecurrence[{3, -3, 1}, {17, 65, 145}, 40] (* _Vincenzo Librandi_, Feb 08 2012 *)
%t A108211 16*Range[50]^2+1 (* _Harvey P. Dale_, Jun 06 2025 *)
%o A108211 (PARI) a(n)= 16*n^2+1 \\ _Charles R Greathouse IV_, Dec 23 2011
%o A108211 (Magma) I:=[17, 65, 145]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 08 2012
%Y A108211 Cf. A002522, A005843, A016802, A053755, A074377, A158488.
%K A108211 nonn,easy
%O A108211 1,1
%A A108211 _Reinhard Zumkeller_, Jun 15 2005