A130782 Period 5, repeat [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, 1, 2, 1, 1, 1

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

Michael Somos, Rational Function Multiplicative Coefficients

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

Formula

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 * A364358 A055457 A277873

Adjacent sequences: A130779 A130780 A130781 * A130783 A130784 A130785

Keyword

nonn,easy

Author

Paul Curtz, Jul 15 2007

Status

approved