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%I #44 Dec 12 2023 09:29:26
%S 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,
%T 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,
%U 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
%N Period 5, repeat [1, 1, 2, 1, 1].
%C Continued fraction expansion of (4 + sqrt(65))/7. - _Klaus Brockhaus_, Apr 30 2010
%H Antti Karttunen, <a href="/A130782/b130782.txt">Table of n, a(n) for n = 0..4999</a>
%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/rfmc.html">Rational Function Multiplicative Coefficients</a>
%H <a href="/index/Rec"order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F a(n) = floor((n+3)/5) - ceiling((n-7)/5). - _Wesley Ivan Hurt_, Mar 27 2014
%F G.f.: (x^4 + x^3 + 2*x^2 + x + 1)/(1-x^5). - _Ralf Stephan_, Mar 28 2014
%F Euler transform of length 5 sequence [1, 1, -1, -1, 1]. - _Michael Somos_, Jun 17 2015
%F Moebius transform is length 10 sequence [1, -1, 0, 0, 1, 0, 0, 0, 0, -1]. - _Michael Somos_, Jun 17 2015
%F 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
%F 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
%F a(n) = a(-n) = a(n+5) for all n in Z. - _Michael Somos_, Jun 17 2015
%e 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
%e G.f. = 1 + x + 2*x^2 + x^3 + x^4 + x^5 + x^6 + 2*x^7 + x^8 + x^9 + ...
%e G.f. = q + q^3 + 2*q^5 + q^7 + q^9 + q^11 + q^13 + 2*q^15 + q^17 + ...
%p A130782:=n->floor((n + 3)/5) - ceil((n - 7)/5); seq(A130782(n), n=0..100); # _Wesley Ivan Hurt_, Mar 27 2014
%t Table[Floor[(n + 3)/5] - Ceiling[(n - 7)/5], {n, 0, 100}] (* _Wesley Ivan Hurt_, Mar 27 2014 *)
%t PadRight[{},150,{1,1,2,1,1}] (* _Harvey P. Dale_, Mar 13 2016 *)
%o (PARI) a(n)=1+(n%5==2) \\ _Charles R Greathouse IV_, Jun 02 2011
%o (Magma) &cat[[1,1,2,1,1]^^25]; // _Vincenzo Librandi_, Feb 25 2016
%Y Cf. A176976 (decimal expansion of (4 + sqrt(65))/7). - _Klaus Brockhaus_, Apr 30 2010
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Jul 15 2007
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