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A265888 a(n) = n + floor(n/4)*(-1)^(n mod 4). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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

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 * A095721 A072061 A255557

Adjacent sequences:  A265885 A265886 A265887 * A265889 A265890 A265891

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Dec 18 2015

STATUS

approved

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Last modified February 21 01:29 EST 2019. Contains 320364 sequences. (Running on oeis4.)