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A186813 a(n) = n if n odd, a(2n) = 3n if n odd, a(4n) = 2n. 2
0, 1, 3, 3, 2, 5, 9, 7, 4, 9, 15, 11, 6, 13, 21, 15, 8, 17, 27, 19, 10, 21, 33, 23, 12, 25, 39, 27, 14, 29, 45, 31, 16, 33, 51, 35, 18, 37, 57, 39, 20, 41, 63, 43, 22, 45, 69, 47, 24, 49, 75, 51, 26, 53, 81, 55, 28, 57, 87, 59, 30, 61, 93, 63, 32, 65, 99, 67, 34, 69, 105, 71, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..72.

M. Somos, Rational Function Multiplicative Coefficients

Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).

FORMULA

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

Euler transform of length 6 sequence [ 3, -3, 1, 2, 0, -1].

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

G.f.: x * (1 - x^2)^3 * (1 - x^6) / ((1 - x)^3 * (1 - x^3) * (1 - x^4)^2). - Michael Somos, May 04 2015

G.f.: f(x) - f(-x^2) where f(x) := x / (1 - x)^2. - Michael Somos, May 04 2015

a(n) = -a(-n) for all n in Z. a(n) = n/2 * A068073(n).

a(n) = n*(4-i^n-(-i)^n)/4 with i=sqrt(-1). - Bruno Berselli, Mar 10 2011

a(n) = A134172(n) + A134172(n+1). - Michael Somos, May 04 2015

a(n) = -(-1)^n * A186111(n). - Michael Somos, May 07 2015

EXAMPLE

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

MATHEMATICA

CoefficientList[Series[x(1+x)(1+x^3)/((1-x)(1+x^2))^2, {x, 0, 80}], x] (* Harvey P. Dale, Mar 06 2011 *)

a[ n_] := n/2 {2, 3, 2, 1}[[ Mod[ n, 4, 1]]]; (* Michael Somos, May 04 2015 *)

PROG

(PARI) {a(n) = n/2 * [ 1, 2, 3, 2][n%4 + 1]};

(PARI) {a(n) = sign(n) * polcoeff( x * (1 + x) * (1 + x^3) / ((1 - x) * (1 + x^2))^2 + x * O(x^abs(n)), abs(n))};

CROSSREFS

Cf. A068073, A134172, A186111.

Cf. A187601. - Bruno Berselli, Mar 12 2011

Sequence in context: A070163 A083343 A186111 * A110898 A264756 A267942

Adjacent sequences:  A186810 A186811 A186812 * A186814 A186815 A186816

KEYWORD

nonn,mult

AUTHOR

Michael Somos, Feb 27 2011

STATUS

approved

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Last modified December 3 17:01 EST 2016. Contains 278745 sequences.