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 A081347 #16 Aug 13 2025 15:41:33
%S A081347 1,2,3,12,13,30,31,56,57,90,91,132,133,182,183,240,241,306,307,380,
%T A081347 381,462,463,552,553,650,651,756,757,870,871,992,993,1122,1123,1260,
%U A081347 1261,1406,1407,1560,1561,1722,1723,1892,1893,2070,2071,2256,2257,2450,2451
%N A081347 First column in maze arrangement of natural numbers.
%C A081347 Interleaves two times the hexagonal numbers A000384 with A054554.
%H A081347 Vincenzo Librandi, <a href="/A081347/b081347.txt">Table of n, a(n) for n = 0..1000</a>
%H A081347 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A081347 a(n) = ((1+2*n^2)+(1-2*n)*(-1)^n)/2.
%F A081347 a(2n) = A054554(n).
%F A081347 a(2n+1) = 2*A000384(n).
%F A081347 G.f.: (1+x-x^2+7*x^3)/((1-x)^3*(1+x)^2). [_Colin Barker_, Apr 17 2012]
%e A081347 Starting with 1,2,3, turn (LL) and then repeat (RRR)(LLL) to get
%e A081347 1 6 7 20
%e A081347 2 5 8 19
%e A081347 3 4 9 18
%e A081347 12 11 10 17
%t A081347 CoefficientList[Series[(1 + x - x^2 + 7 x^3) / ((1 - x)^3 (1 + x)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%t A081347 LinearRecurrence[{1,2,-2,-1,1},{1,2,3,12,13},60] (* _Harvey P. Dale_, Aug 13 2025 *)
%o A081347 (Magma) [((1+2*n^2)+(1-2*n)*(-1)^n)/2: n in [0..50]]; // _Vincenzo Librandi_, Aug 08 2013
%Y A081347 Cf. A081348, A080335.
%K A081347 easy,nonn
%O A081347 0,2
%A A081347 _Paul Barry_, Mar 19 2003