cp's OEIS Frontend

A110659 a(n) = A028242(A110654(n)).

%I A110659 #33 Jan 03 2023 05:38:15
%S A110659 1,0,0,2,2,1,1,3,3,2,2,4,4,3,3,5,5,4,4,6,6,5,5,7,7,6,6,8,8,7,7,9,9,8,
%T A110659 8,10,10,9,9,11,11,10,10,12,12,11,11,13,13,12,12,14,14,13,13,15,15,14,
%U A110659 14,16,16,15,15,17,17,16,16,18,18,17,17,19,19,18,18,20,20,19,19,21,21,20
%N A110659 a(n) = A028242(A110654(n)).
%H A110659 G. C. Greubel, <a href="/A110659/b110659.txt">Table of n, a(n) for n = 0..1000</a>
%H A110659 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A110659 a(n) = floor(n/4) - (n mod 4) mod 3 + floor((2 + n mod 4)/2).
%F A110659 a(n) = (2*n + 3 + 6*cos(n*Pi/2) - cos(n*Pi) - 6*sin(n*Pi/2))/8. - _Wesley Ivan Hurt_, Oct 01 2017
%F A110659 a(n + 4) = a(n) + 1 so a(n + 8) = 2 * a(n + 4) - a(n). - _David A. Corneth_, Oct 02 2017
%F A110659 G.f.: (1 + 2*x^3 - x - x^4)/((1 + x)*(1 - x)^2*(1 + x^2)). - _R. J. Mathar_, May 22 2019
%F A110659 E.g.f.: (3*cos(x) + cosh(x)*(1 + x) - 3*sin(x) + (2 + x)*sinh(x))/4. - _Stefano Spezia_, Jan 03 2023
%t A110659 A028242[n_] := (1 + 2*n + 3*(-1)^n)/4; Table[A028242[Ceiling[n/2]], {n, 0, 100}] (* _G. C. Greubel_, Sep 03 2017 *)
%t A110659 LinearRecurrence[{1,0,0,1,-1},{1,0,0,2,2},100] (* _Harvey P. Dale_, Jul 05 2020 *)
%o A110659 (PARI) vector(100, n, n--; (1/4)*(1 + 2*ceil(n/2) + 3*(-1)^(ceil(n/2)))) \\ _G. C. Greubel_, Sep 03 2017
%o A110659 (PARI) a(n) = (n\4) + [1,0,0,2][1+n%4] \\ _David A. Corneth_, Oct 02 2017
%o A110659 (PARI) first(n) = my(c = res = [1,0,0,2]); for(i=1,(n-1)\4, c += [1,1,1,1]; res = concat(res, c)); res \\ _David A. Corneth_, Oct 02 2017
%o A110659 (Magma) b:= func< n | (1 + 2*n + 3*(-1)^n)/4 >; [b(Ceiling(n/2)): n in [0..100]]; // _G. C. Greubel_, May 22 2019
%o A110659 (Sage) ((1+2*x^3-x-x^4)/((1-x)*(1-x^4))).series(x, 100).coefficients(x, sparse=False) # _G. C. Greubel_, May 22 2019
%Y A110659 Cf. A008624, A028242, A110654.
%K A110659 nonn,easy
%O A110659 0,4
%A A110659 _Reinhard Zumkeller_, Aug 05 2005