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Numerator of (n-1) * ceiling(n/2) / n.
1

%I #16 Dec 05 2023 18:25:57

%S 0,1,4,3,12,5,24,7,40,9,60,11,84,13,112,15,144,17,180,19,220,21,264,

%T 23,312,25,364,27,420,29,480,31,544,33,612,35,684,37,760,39,840,41,

%U 924,43,1012,45,1104,47,1200,49,1300,51,1404,53,1512,55,1624,57,1740,59,1860,61,1984,63,2112,65

%N Numerator of (n-1) * ceiling(n/2) / n.

%C A046092 Union A005408.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).

%F a(2n) = 2n-1. a(2n-1) = 2n(n-1).

%F a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: x^2*(x^4-4*x-1) / ((x-1)^3*(x+1)^3). - _Colin Barker_, Apr 02 2014

%F a(n) = n - 1 + (2*floor((n+2)/2)^2 - 2*floor((n+2)/2) - n + 1) * (n mod 2). - _Wesley Ivan Hurt_, Apr 02 2014

%F a(n) = (n-1)*(n+3-(n-1)*(-1)^n)/4. - _Wesley Ivan Hurt_, Dec 05 2023

%p A240134:=n->numer( (n-1)*ceil(n/2) / n ); seq(A240134(n), n=1..100);

%t Table[Numerator[(n - 1) Ceiling[n/2] / n], {n, 100}]

%o (PARI) concat(0, Vec(x^2*(x^4-4*x-1)/((x-1)^3*(x+1)^3) + O(x^100))) \\ _Colin Barker_, Apr 02 2014

%o (Magma) [(n-1)*(n+3-(n-1)*(-1)^n)/4 : n in [1..80]]; // _Wesley Ivan Hurt_, Dec 05 2023

%Y Bisections: A046092 and A005408.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Apr 02 2014