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
Examples
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 + ...
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).
Crossrefs
Cf. A176976 (decimal expansion of (4 + sqrt(65))/7). - Klaus Brockhaus, Apr 30 2010
Programs
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Magma
&cat[[1,1,2,1,1]^^25]; // Vincenzo Librandi, Feb 25 2016
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Maple
A130782:=n->floor((n + 3)/5) - ceil((n - 7)/5); seq(A130782(n), n=0..100); # Wesley Ivan Hurt, Mar 27 2014
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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 *) -
PARI
a(n)=1+(n%5==2) \\ Charles R Greathouse IV, Jun 02 2011
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
Comments