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

0,3

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).

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.

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]

Prog

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

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).

Sequence in context: A255558 A072062 A002192 * A340709 A095721 A072061

Adjacent sequences: A265885 A265886 A265887 * A265889 A265890 A265891

Keyword

nonn,easy

Author

Bruno Berselli, Dec 18 2015

Status

approved