A265888 a(n) = n + floor(n/4)*(-1)^(n mod 4).

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, 32, 21, 35, 22, 37, 24, 40, 25, 42, 27, 45, 28, 47, 30, 50, 31, 52, 33, 55, 34, 57, 36, 60, 37, 62, 39, 65, 40, 67, 42, 70, 43, 72, 45, 75, 46, 77, 48, 80, 49, 82, 51, 85, 52, 87

Offset: 0

Author

Bruno Berselli, Dec 18 2015

Keywords

• nonn
• easy

Comments

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

a(n) = n + floor(n/4)*(-1)^(n mod 2). - Chai Wah Wu, Jan 29 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).

Crossrefs

Cf. A047202, A047624.

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

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

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

Programs

Magma

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

Mathematica

Table[n + Floor[n/4] (-1)^Mod[n, 4], {n, 0, 70}]
LinearRecurrence[{0, 1, 0, 1, 0, -1}, {0, 1, 2, 3, 5, 4}, 80]

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

Python

def A265888(n): return n+(-(n>>2) if n&1 else n>>2) # Chai Wah Wu, Jan 29 2023

Sage

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

Formula

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

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

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

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