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 A081353 #22 Sep 08 2022 08:45:09
%S A081353 3,5,13,19,31,41,57,71,91,109,133,155,183,209,241,271,307,341,381,419,
%T A081353 463,505,553,599,651,701,757,811,871,929,993,1055,1123,1189,1261,1331,
%U A081353 1407,1481,1561,1639,1723,1805,1893,1979,2071,2161,2257,2351,2451,2549
%N A081353 Diagonal of square maze arrangement of natural numbers A081349.
%H A081353 Vincenzo Librandi, <a href="/A081353/b081353.txt">Table of n, a(n) for n = 0..10000</a>
%H A081353 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A081353 a(n) = (n+1)*(n+2)+(-1)^n = 2*binomial(n+2,2)+(-1)^n.
%F A081353 G.f.: (3-x)*(1+x^2)/((1-x)^3*(1+x)). [_Colin Barker_, Sep 03 2012]
%F A081353 From _Wesley Ivan Hurt_, Aug 09 2015: (Start)
%F A081353 a(n) = 2*a(n-1)-2*a(n-3)+a(n-4), n>4.
%F A081353 a(n) = n^2+3n+3 if n is even, otherwise n^2+3n+1.
%F A081353 a(n) = A137932(n+3) - A109613(n+1). (End)
%p A081353 A081353:=n->(n+1)*(n+2)+(-1)^n: seq(A081353(n), n=0..100); # _Wesley Ivan Hurt_, Aug 09 2015
%t A081353 Table[(n + 1) (n + 2) + (-1)^n, {n, 0, 70}] (* _Wesley Ivan Hurt_, Aug 09 2015 *)
%t A081353 LinearRecurrence[{2,0,-2,1},{3,5,13,19},50] (* _Harvey P. Dale_, Aug 02 2021 *)
%o A081353 (Magma) [(n + 1)*(n + 2) + (-1)^n: n in [0..50]]; // _Vincenzo Librandi_, Sep 06 2011
%Y A081353 Cf. A081349, A081350, A081351, A081352.
%Y A081353 Cf. A109613, A137932.
%Y A081353 Bisections are in A054554, A125202.
%K A081353 nonn,easy
%O A081353 0,1
%A A081353 _Paul Barry_, Mar 19 2003