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A186187 Period 8 sequence [ 2, 2, 1, 2, 4, 2, 1, 2, ...] except a(0) = 1. 0
1, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also continued fraction expansion of sqrt(2717)/38.  - Bruno Berselli, Mar 07 2011

LINKS

Table of n, a(n) for n=0..104.

Michael Somos, Rational Function Multiplicative Coefficients

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

FORMULA

Euler transform of length 8 sequence [ 2, -2, 2, 0, 0, -2, 0, 1].

Moebius transform is length 8 sequence [ 2, -1, 0, 3, 0, 0, 0, -2].

a(n) = 2 * b(n) where b() is multiplicative with b(2) = 1/2, b(4) = 2, b(2^e) = 1 if e>2, b(p^e) = 1 if p>2.

G.f.: (1 + x)^4 * (1 - x + x^2)^2 / (1 - x^8). a(-n) = a(n). a(2*n + 1) = 2, a(4*n + 2) = 1, a(8*n + 4) = 4, a(8*n) = 2 except a(0) = 1.

a(n) = A056594(n)-A014017(n)+2 for n>0.  - Bruno Berselli, Feb 15 2011

EXAMPLE

1 + 2*x + x^2 + 2*x^3 + 4*x^4 + 2*x^5 + x^6 + 2*x^7 + 2*x^8 + 2*x^9 + ...

MATHEMATICA

PadRight[{1}, 108, {2, 2, 1, 2, 4, 2, 1, 2}] (* Harvey P. Dale, Mar 22 2012 *)

PROG

(PARI) {a(n) = - (n==0) + [ 2, 2, 1, 2, 4, 2, 1, 2] [n%8 + 1]}

(PARI) {a(n) = polcoeff( (1 + x)^4 * (1 - x + x^2)^2 / (1 - x^8) + x * O(x^abs(n)), abs(n))}

(MAGMA)  [1] cat &cat[ [2, 1, 2, 4, 2, 1, 2, 2]: n in [1..13]];  //  Bruno Berselli, Mar 07 2011

CROSSREFS

Sequence in context: A290091 A059149 A273917 * A013943 A164281 A082693

Adjacent sequences:  A186184 A186185 A186186 * A186188 A186189 A186190

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Feb 14 2011

STATUS

approved

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Last modified May 6 17:59 EDT 2021. Contains 343586 sequences. (Running on oeis4.)