login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A255347 a(n) = n * (1 - (-1)^(n/4) / 4) if n divisible by 4, a(n) = n otherwise. 1
0, 1, 2, 3, 5, 5, 6, 7, 6, 9, 10, 11, 15, 13, 14, 15, 12, 17, 18, 19, 25, 21, 22, 23, 18, 25, 26, 27, 35, 29, 30, 31, 24, 33, 34, 35, 45, 37, 38, 39, 30, 41, 42, 43, 55, 45, 46, 47, 36, 49, 50, 51, 65, 53, 54, 55, 42, 57, 58, 59, 75, 61, 62, 63, 48, 65, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

M. Somos, Rational Function Multiplicative Coefficients

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,-2,4,-2,0,-1,2,-1).

FORMULA

Euler transform of length 10 sequence [2, 0, 1, -2, 1, -1, 0, 2, 0, -1].

a(n) is multiplicative with a(2) = 2, a(4) = 5, a(2^e) = 3*2^(e-1) if e>2, a(p^e) = p^e otherwise.

G.f.: f(x) - f(-x^4) where f(x) := x / (1 - x)^2.

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

a(n) = -a(-n) for all n in Z.

EXAMPLE

G.f. = x + 2*x^2 + 3*x^3 + 5*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 6*x^8 + 9*x^9 + ...

MATHEMATICA

a[ n_] := n {1, 1, 1, 5/4, 1, 1, 1, 3/4}[[Mod[ n, 8, 1]]];

a[ n_] := n If[ Divisible[ n, 4], 1 - (-1)^(n/4) / 4, 1];

LinearRecurrence[{2, -1, 0, -2, 4, -2, 0, -1, 2, -1}, {0, 1, 2, 3, 5, 5, 6, 7, 6, 9}, 70] (* Harvey P. Dale, Jul 28 2018 *)

CoefficientList[Series[x*(1+x^3)*(1+x^5)/((1-x)^2*(1+x^4)^2), {x, 0, 60}], x] (* G. C. Greubel, Aug 02 2018 *)

PROG

(PARI) {a(n) = n * if( n%4, 1, 1 - (-1)^(n/4) / 4)};

(PARI) {a(n) = n * [3/4, 1, 1, 1, 5/4, 1, 1, 1][n%8 + 1]};

(PARI) x='x+O('x^60); concat([0], Vec(x*(1+x^3)*(1+x^5)/((1-x)^2*(1 + x^4)^2))) \\ G. C. Greubel, Aug 02 2018

(MAGMA) m:=60; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+x^3)*(1+x^5)/((1-x)^2*(1+x^4)^2))); // G. C. Greubel, Aug 02 2018

CROSSREFS

Sequence in context: A169787 A165959 A111164 * A029910 A063677 A078903

Adjacent sequences:  A255344 A255345 A255346 * A255348 A255349 A255350

KEYWORD

nonn,mult,easy

AUTHOR

Michael Somos, May 04 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)