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 A267942 #23 Sep 08 2022 08:46:15
%S A267942 3,3,2,6,3,11,6,18,11,27,18,38,27,51,38,66,51,83,66,102,83,123,102,
%T A267942 146,123,171,146,198,171,227,198,258,227,291,258,326,291,363,326,402,
%U A267942 363,443,402,486,443,531,486,578,531,627,578,678,627,731,678,786,731
%N A267942 Interleave (n-1)^2 + 2 and (n+1)^2 + 2.
%C A267942 Trisections:
%C A267942 3, 6, 6, 27, 27, 66, 66, ... = 3*(1, 2, 2, 9, 9, 22, 22, ... ). See A056105.
%C A267942 3, 3, 18, 18, 51, 51, 102, ... = 3*(1, 1, 6, 6, 17, 17, ... ). See A056109.
%C A267942 2, 11, 11, 38, 38, 83, 83, ... (== 2 (mod 9)).
%C A267942 The trisections also have the signature (1,2,-2,-1,1). The corresponding main sequence is 0, 0, 0, 0, 1, 1, 3, 3, ... = A161680(n) with each term duplicated.
%H A267942 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A267942 a(n) = (A261327(n+2) + A261327(n-3))/5.
%F A267942 a(n+1) = a(n) + (-1)^n * A022998(n), a(0)=3.
%F A267942 a(n+3) = a(n) + 3*A193356(n), a(0)=a(1)=3, a(2)=2.
%F A267942 a(n) = 3 + A174474(n).
%F A267942 a(2n) + a(2n+1) = A255844(n).
%F A267942 From _Colin Barker_, Jan 22 2016: (Start)
%F A267942 a(n) = (2*n^2 - 6*(-1)^n*n - 2*n + 3*(-1)^n + 21)/8.
%F A267942 a(n) = (n^2 - 4*n + 12)/4 for n even.
%F A267942 a(n) = (n^2 + 2*n + 9)/4 for n odd.
%F A267942 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 4.
%F A267942 G.f.: (3 - 7*x^2 + 4*x^3 + 2*x^4) / ((1-x)^3*(1+x)^2).
%F A267942 (End)
%e A267942 a(0) = (2+13)/5, a(1) = (13+2)/5, a(2) = (5+5)/5, a(3) = (29+1)/5, ... (using first formula).
%t A267942 Flatten[Table[{n^2 - 2 n + 3, n^2 + 2 n + 3}, {n, 0, 30}]] (* _Vincenzo Librandi_, Jan 23 2016 *)
%t A267942 CoefficientList[Series[(3 - 7 x^2 + 4 x^3 + 2 x^4)/((1 - x)^3 (1 + x)^2), {x, 0, 56}], x] (* _Michael De Vlieger_, Jan 24 2016 *)
%o A267942 (PARI) Vec((3-7*x^2+4*x^3+2*x^4)/((1-x)^3*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jan 22 2016
%o A267942 (Magma) &cat [[(n-1)^2+2, (n+1)^2+2]: n in [0..50]]; // _Vincenzo Librandi_, Jan 23 2016
%Y A267942 Cf. A000290, A007395, A010701, A022998, A056105, A056109, A059100, A161680, A174474, A193356, A255844, A261327.
%K A267942 nonn,easy
%O A267942 0,1
%A A267942 _Paul Curtz_, Jan 22 2016
%E A267942 More terms from _Colin Barker_, Jan 22 2016