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A130782 Periodic sequence with period 1, 1, 2, 1, 1. 5
1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Continued fraction expansion of (4 + sqrt(65))/7. - Klaus Brockhaus, Apr 30 2010

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..4999

M. Somos, Rational Function Multiplicative Coefficients

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

FORMULA

a(n) = (1/25)*{3*(n mod 5)+3*[(n+1) mod 5]+8*[(n+2) mod 5]-2*[(n+3) mod 5]+3*[(n+4) mod 5]}, with n>=0. - Paolo P. Lava, Aug 28 2007

a(n) = floor((n + 3)/5) - ceiling((n - 7)/5). - Wesley Ivan Hurt, Mar 27 2014

G.f.: (x^4 + x^3 + 2*x^2 + x + 1)/(1-x^5). - Ralf Stephan, Mar 28 2014

Euler transform of length 5 sequence [ 1, 1, -1, -1, 1]. - Michael Somos, Jun 17 2015

Moebius transform is length 10 sequence [ 1, -1, 0, 0, 1, 0, 0, 0, 0, -1]. - Michael Somos, Jun 17 2015

G.f.: Sum_{k>0} a(2*k-1) * q^n = f(q) + f(q^5) where f(q) := q / (1 - q^2). - Michael Somos, Jun 17 2015

a(n) = b(2*n + 1) where b() is multiplicative with b(2^e) = 0^3, b(5^e) = 2 if e>0, b(p^e) = 1 otherwise. - Michael Somos, Jun 17 2015

a(n) = a(-n) = a(n+5) for all n in Z. - Michael Somos, Jun 17 2015

EXAMPLE

a(5) = floor((5 + 3)/5) - ceiling((5 - 7)/5) = floor(8/5) - ceil(-2/5) = floor(8/5) + floor(2/5) = 1 + 0 = 1. - Wesley Ivan Hurt, Mar 27 2014

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

G.f. = q + q^3 + 2*q^5 + q^7 + q^9 + q^11 + q^13 + 2*q^15 + q^17 + ...

MAPLE

A130782:=n->floor((n + 3)/5) - ceil((n - 7)/5); seq(A130782(n), n=0..100); # Wesley Ivan Hurt, Mar 27 2014

MATHEMATICA

Table[Floor[(n + 3)/5] - Ceiling[(n - 7)/5], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 27 2014 *)

PadRight[{}, 150, {1, 1, 2, 1, 1}] (* Harvey P. Dale, Mar 13 2016 *)

PROG

(PARI) a(n)=1+(n%5==2) \\ Charles R Greathouse IV, Jun 02 2011

(MAGMA) &cat[[1, 1, 2, 1, 1]^^25]; // Vincenzo Librandi, Feb 25 2016

CROSSREFS

Cf. A176976 (decimal expansion of (4 + sqrt(65))/7). - Klaus Brockhaus, Apr 30 2010

Sequence in context: A280569 A140345 A177706 * A055457 A277873 A032542

Adjacent sequences:  A130779 A130780 A130781 * A130783 A130784 A130785

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jul 15 2007

STATUS

approved

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Last modified July 23 13:49 EDT 2019. Contains 325254 sequences. (Running on oeis4.)