A242112 a(n) = floor((2*n+6)/(5-(-1)^n)).

1, 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 4, 7, 5, 8, 6, 9, 6, 10, 7, 11, 8, 12, 8, 13, 9, 14, 10, 15, 10, 16, 11, 17, 12, 18, 12, 19, 13, 20, 14, 21, 14, 22, 15, 23, 16, 24, 16, 25, 17, 26, 18, 27, 18, 28, 19, 29, 20, 30, 20, 31, 21, 32, 22, 33, 22, 34, 23, 35, 24, 36

Offset: 0

Author

Wesley Ivan Hurt, Aug 21 2014

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1,0,-1).

Crossrefs

Cf. A010693, A093718.

Programs

Magma

[Floor((2*n+6)/(5-(-1)^n)) : n in [0..100]];

Magma

[IsEven(n) select 1+n/2 else 1+Floor(n/3): n in [0..80]]; // Bruno Berselli, Aug 22 2014

Maple

A242112:=n->floor((2*n+6)/(5-(-1)^n)): seq(A242112(n), n=0..100);

Mathematica

Table[Floor[(2 n + 6)/(5 - (-1)^n)], {n, 0, 100}]
LinearRecurrence[{0,1,0,0,0,1,0,-1},{1,1,2,2,3,2,4,3},80] (* Harvey P. Dale, Oct 24 2017 *)

Formula

a(n) = a(n-2) + a(n-6) - a(n-8).

a(n) = ( n+3 - A093718(n) ) / A010693(n).

From Robert Israel, Aug 22 2014: (Start)

a(n) = sqrt(3)/18*(sin(2*n*Pi/3)+sin(n*Pi/3)) + 1/6*(cos(2*n*Pi/3)-cos(n*Pi/3)) + (-1)^n*(2+n)/12 + 5*(n+2)/12.

G.f.: (1 + x + x^2 + x^3 + x^4)/(1 - x^2 - x^6 + x^8). (End)

a(n) = 1 + n/2 if n is even, otherwise a(n) = 1 + floor(n/3). - Bruno Berselli, Aug 22 2014