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 A247617 #29 Sep 08 2022 08:46:09
%S A247617 1,5,3,7,1,9,5,11,3,13,7,15,3,17,9,19,5,21,11,23,5,25,13,27,7,29,15,
%T A247617 31,7,33,17,35,9,37,19,39,9,41,21,43,11,45,23,47,11,49,25,51,13,53,27,
%U A247617 55,13,57,29,59,15,61,31,63,15,65,33,67
%N A247617 a(4n) = n + 1/2 - (-1)^n/2 + (-1)^n, a(2n+1) = 2*n + 5, a(4n+2) = 2*n + 3.
%C A247617 Essentially a permutation of A129756 (odd numbers repeated four times).
%C A247617 a(-1) = 3, a(-2) = a(-3) = 1.
%C A247617 Distance between the first two (2*k+1)'s: 2*k+1 terms. Distance between the last two (2*n+1)'s: 4 terms. Essentially same distances as in -a(-n) = -1, -3, -1, -1, 1, 1, 1, 3, 1, 5, 3, 7, 3, 9, 5, 11, 3, 13, 7, 15, 5, 17, 9, 19, 5, 21, 11, 23, 7, 25, 13, 27, 7, ... .
%H A247617 G. C. Greubel, <a href="/A247617/b247617.txt">Table of n, a(n) for n = 0..5000</a>
%H A247617 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,0,0,1,0,0,0,-1).
%F A247617 a(n) = a(n-4) + a(n-8) - a(n-12).
%F A247617 a(n) * A246416(n) = A061037(n+2).
%F A247617 A246416(n+4) - a(n) = sequence of period 4: [1, 0, 0, 0].
%F A247617 a(n+4) - a(n) = sequence of period 8: [0, 4, 2, 4, 2, 4, 2, 4].
%F A247617 G.f.: -(3*x^11+x^10+x^9-x^8-4*x^7-2*x^6-4*x^5-7*x^3-3*x^2-5*x-1) / ((x-1)^2*(x+1)^2*(x^2+1)^2*(x^4+1)). - _Colin Barker_, Sep 21 2014
%F A247617 a(n) = a(n-8) + sequence of period 4: [2, 8, 4, 8] (= 2*A176895(n)).
%F A247617 a(-n) * A246416(-n) = A061037(n-2).
%F A247617 a(n) = (n+4)*(1-ceiling((2-n)/4)-ceiling((n-2)/4))/2+(n+4)*(1+floor((1-n)/2)+floor((n-1)/2))-(n+2+2(-1)^(n/4))*(ceiling(n/4)-floor(n/4)-1)/4. - _Wesley Ivan Hurt_, Sep 21 2014
%p A247617 A247617:=n->(n+4)*(1-ceil((2-n)/4)-ceil((n-2)/4))/2+(n+4)*(1+floor((1-n)/2)+floor((n-1)/2))-(n+2+2*(-1)^(n/4))*(ceil(n/4)-floor(n/4)-1)/4: seq(A247617(n), n=0..50); # _Wesley Ivan Hurt_, Sep 21 2014
%t A247617 Table[(n + 4) (1 - Ceiling[(2 - n)/4] - Ceiling[(n - 2)/4])/2 + (n + 4) (1 + Floor[(1 - n)/2] + Floor[(n - 1)/2]) - (n + 2 + 2 (-1)^(n/4)) (Ceiling[n/4] - Floor[n/4] - 1)/4, {n, 0, 50}] (* _Wesley Ivan Hurt_, Sep 21 2014 *)
%o A247617 (PARI) Vec(-(3*x^11+x^10+x^9-x^8-4*x^7-2*x^6-4*x^5-7*x^3-3*x^2-5*x-1)/((x-1)^2*(x+1)^2*(x^2+1)^2*(x^4+1)) + O(x^100)) \\ _Colin Barker_, Sep 21 2014
%o A247617 (Magma) I:=[1,5,3,7,1,9,5,11,3,13,7,15]; [n le 12 select I[n] else Self(n-4)+Self(n-8)-Self(n-12): n in [1..80]]; // _Vincenzo Librandi_, Oct 15 2014
%Y A247617 Cf. A010709, A061037, A121262, A129756, A176895, A246416.
%K A247617 nonn,easy
%O A247617 0,2
%A A247617 _Paul Curtz_, Sep 21 2014