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%I #35 Dec 14 2023 05:21:17
%S 0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,
%T 0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,
%U 1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1
%N Single paradiddle. In percussion, the paradiddle is a four-note drum sticking pattern consisting of two alternating notes followed by two notes on the same hand.
%C Also the binary expansion of the constant 5/17 = 2^(-2) + 2^(-5) + 2^(-7) + ... - _R. J. Mathar_, Mar 27 2009
%C Period 8: repeat [0, 1, 0, 0, 1, 0, 1, 1]. - _Wesley Ivan Hurt_, Aug 23 2015
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Paradiddle">Paradiddle</a>
%H <a href="/index/Mu#music">Index entries for sequences related to music</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1,1).
%F From _R. J. Mathar_, Mar 27 2009: (Start)
%F a(n) = a(n-8) = a(n-1) - a(n-4) + a(n-5).
%F G.f.: -x*(1+x^3-x)/((x-1)*(1+x^4)). (End)
%F a(n) = (1-(-1)^((n+5)*(n+6)*(n^2+11*n+32)/8))/2. - _Wesley Ivan Hurt_, Aug 23 2015
%F a(n) = A165211(n+5). - _Wesley Ivan Hurt_, Aug 23 2015
%p A130198:= n -> [0, 1, 0, 0, 1, 0, 1, 1][(n mod 8)+1]: seq(A130198(n), n=0..100); # _Wesley Ivan Hurt_, Aug 23 2015
%t CoefficientList[Series[x*(1 - x + x^3)/((1 - x)*(1 + x^4)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Aug 23 2015 *)
%o (PARI) a(n)=((n%8>3)+(n%4==1))%2 \\ _Jaume Oliver Lafont_, Mar 19 2009]
%o (PARI) a(n)=210\2^(n%8)%2; \\ _Jaume Oliver Lafont_, Mar 24 2009]
%o (PARI) apply( A130198(n)=bittest(210,n%8), [0..99]) \\ _M. F. Hasler_, May 24 2019
%o (Magma) [(1-(-1)^((n+5)*(n+6)*(n^2+11*n+32) div 8))/2 : n in [0..100]]; // _Wesley Ivan Hurt_, Aug 23 2015
%Y Cf. A121262, A131078. - _Jaume Oliver Lafont_, Mar 19 2009
%Y Cf. A165211.
%K nonn,easy
%O 0,1
%A _Simone Severini_, May 16 2007
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