A265888 - OEIS

%I #24 Jan 29 2023 23:00:58

%S 0,1,2,3,5,4,7,6,10,7,12,9,15,10,17,12,20,13,22,15,25,16,27,18,30,19,

%T 32,21,35,22,37,24,40,25,42,27,45,28,47,30,50,31,52,33,55,34,57,36,60,

%U 37,62,39,65,40,67,42,70,43,72,45,75,46,77,48,80,49,82,51,85,52,87

%N a(n) = n + floor(n/4)*(-1)^(n mod 4).

%C This sequence does not include the numbers of the type 3*A047202(n)+2.

%C a(n) = n + floor(n/4)*(-1)^(n mod 2). - _Chai Wah Wu_, Jan 29 2023

%H G. C. Greubel, <a href="/A265888/b265888.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,-1).

%F G.f.: x*(1 + 2*x + 2*x^2 + 3*x^3)/((1 + x^2)*(1 - x^2)^2).

%F a(n) = a(n-2) + a(n-4) - a(n-6) for n>5.

%F a(n+1) + a(n) = A047624(n+1).

%F a(4*k+r) = (4+(-1)^r)*k + r mod 3, where r = 0..3.

%t Table[n + Floor[n/4] (-1)^Mod[n, 4], {n, 0, 70}]

%t LinearRecurrence[{0, 1, 0, 1, 0, -1}, {0, 1, 2, 3, 5, 4}, 80]

%o (Sage) [n+floor(n/4)*(-1)^mod(n, 4) for n in (0..70)]

%o (Magma) [n+Floor(n/4)*(-1)^(n mod 4): n in [0..70]];

%o (PARI) x='x+O('x^100); concat(0, Vec(x*(1+2*x+2*x^2+3*x^3)/((1+x^2)*(1- x^2)^2))) \\ _Altug Alkan_, Dec 22 2015

%o (Python)

%o def A265888(n): return n+(-(n>>2) if n&1 else n>>2) # _Chai Wah Wu_, Jan 29 2023

%Y Cf. A047202, A047624.

%Y Cf. A064455: n+floor(n/2)*(-1)^(n mod 2).

%Y Cf. A265667: n+floor(n/3)*(-1)^(n mod 3).

%Y Cf. A265734: n+floor(n/5)*(-1)^(n mod 5).

%K nonn,easy

%O 0,3

%A _Bruno Berselli_, Dec 18 2015