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A214392 If n mod 4 = 0 then a(n) = n/4, otherwise a(n) = n. 4
0, 1, 2, 3, 1, 5, 6, 7, 2, 9, 10, 11, 3, 13, 14, 15, 4, 17, 18, 19, 5, 21, 22, 23, 6, 25, 26, 27, 7, 29, 30, 31, 8, 33, 34, 35, 9, 37, 38, 39, 10, 41, 42, 43, 11, 45, 46, 47, 12, 49, 50, 51, 13, 53, 54, 55, 14, 57, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equivalent to A065883 for n mod 16 != 0. - Peter Kagey, Sep 02 2015

LINKS

Jeremy Gardiner, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

FORMULA

From Bruno Berselli, Oct 16 2012: (Start)

G.f.: x*(1+2*x+3*x^2+x^3+3*x^4+2*x^5+x^6)/(1-x^4)^2.

a(n) = ( 1 - (3/16)*(1+(-1)^n)*(1+i^(n(n+1))) )*n, where i=sqrt(-1).

a(n) = a(-n) = 2*a(n-4) - a(n-8). (End)

From Werner Schulte, Jul 08 2018: (Start)

a(n) for n > 0 is multiplicative with a(2^e) = 2^e if e < 2 and a(2^e) = 2^(e-2) if e > 1 otherwise a(p^e) = p^e for prime p > 2 and e >= 0.

Dirichlet g.f.: Sum_{n>0} a(n)/n^s = (1-3/4^s)*zeta(s-1).

Dirichlet inverse b(n) is multiplicative with b(2^e) = (-1)^e * A038754(e), e >= 0, and for prime p > 2: b(p) = -p and b(p^e) = 0 if e > 1.

(End)

EXAMPLE

a(16) = 16/4 = 4;

a(17) = 17.

MATHEMATICA

Table[If[Mod[n, 4] == 0, n/4, n], {n, 0, 50}] (* G. C. Greubel, Oct 26 2017 *)

LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {0, 1, 2, 3, 1, 5, 6, 7}, 60] (* Harvey P. Dale, Mar 30 2018 *)

PROG

(PARI) a(n)=if(n%4, n, n/4) \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Cf. A026741, A051176, A186646, A065883, A038754.

Sequence in context: A083346 A319652 A065883 * A071975 A182659 A197701

Adjacent sequences:  A214389 A214390 A214391 * A214393 A214394 A214395

KEYWORD

nonn,easy,mult

AUTHOR

Jeremy Gardiner, Jul 15 2012

STATUS

approved

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Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)