|
%I #41 Oct 04 2022 09:27:51
%S 0,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,8,9,7,8,9,
%T 10,8,9,10,11,9,10,11,12,10,11,12,13,11,12,13,14,12,13,14,15,13,14,15,
%U 16,14,15,16,17,15,16,17,18,16,17,18,19,17,18,19,20,18,19,20,21,19,20,21
%N a(n) = A028242(A028242(n)).
%C Also array read by rows, with four columns, in which row n lists n, n+1, n+2, n. - _Omar E. Pol_, Jan 22 2012
%H Vincenzo Librandi, <a href="/A110657/b110657.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A110658(n) = A028242(a(n)) = a(A028242(n)).
%F a(n) = floor(n/4) + (n mod 4) mod 3.
%F From _Bruno Berselli_, Sep 28 2011: (Start)
%F G.f.: x*(1+x-2*x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2).
%F a(n) = (1/8)*(2*n-6*(-1)^(n*(n+1)/2)+3*(-1)^n+3). (End)
%F From _Wesley Ivan Hurt_, Apr 12 2015: (Start)
%F a(n) = a(n-1)+a(n-4)-a(n-5).
%F a(n) = 1 + floor((n-7)/4) + ((n-7) mod 4). (End)
%F a(n) = n - 3*floor((n+1)/4). - _Gionata Neri_, Oct 19 2015
%F a(n) = (2*n+3-6*cos(n*Pi/2)+3*cos(n*Pi)+6*sin(n*Pi/2))/8. - _Wesley Ivan Hurt_, Oct 01 2017
%F Sum_{n>=4} (-1)^(n+1)/a(n) = 1/2. - _Amiram Eldar_, Oct 04 2022
%e From _Omar E. Pol_, Jan 22 2012: (Start)
%e Array begins:
%e 0, 1, 2, 0;
%e 1, 2, 3, 1;
%e 2, 3, 4, 2;
%e 3, 4, 5, 3;
%e 4, 5, 6, 4;
%e 5, 6, 7, 5;
%e 6, 7, 8, 6;
%e 7, 8, 9, 7;
%e (End)
%p A110657:=n->(1/8)*(2*n-6*(-1)^(n*(n+1)/2)+3*(-1)^n+3): seq(A110657(n), n=0..100); # _Wesley Ivan Hurt_, Apr 12 2015
%t Table[(1/8)*(2*n - 6*(-1)^(n*(n + 1)/2) + 3*(-1)^n + 3), {n, 0, 100}] (* _Wesley Ivan Hurt_, Apr 12 2015 *)
%t LinearRecurrence[{1,0,0,1,-1},{0,1,2,0,1},90] (* _Harvey P. Dale_, Feb 02 2020 *)
%o (Magma) [Integers()!(2*n-6*(-1)^(n*(n+1)/2)+3*(-1)^n+3)/8: n in [0..81]]; // _Bruno Berselli_, Sep 28 2011
%o (PARI) vector(80, n, n--; 1 + (n-7)\4 + ((n-7) % 4)) \\ _Michel Marcus_, Apr 13 2015
%Y Cf. A007892, A110655.
%K nonn,tabf,easy
%O 0,3
%A _Reinhard Zumkeller_, Aug 05 2005
|
