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A130198
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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.
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3
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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Also the binary expansion of the constant 5/17 = 2^(-2) + 2^(-5) + 2^(-7) + ... - R. J. Mathar, Mar 27 2009
Period 8: repeat [0, 1, 0, 0, 1, 0, 1, 1]. - Wesley Ivan Hurt, Aug 23 2015
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LINKS
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Table of n, a(n) for n=0..95.
Wikipedia, Paradiddle
Index entries for sequences related to music
Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).
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FORMULA
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a(n) = (1/56)*(8*(n mod 8) + ((n+1) mod 8) - 6*((n+2) mod 8) + 8*((n+3) mod 8) - 6*((n+4) mod 8) + ((n+5) mod 8) + 8*((n+6) mod 8) - 6*((n+7) mod 8)), with n >= 0. - Paolo P. Lava, Nov 09 2007
From R. J. Mathar, Mar 27 2009: (Start)
a(n) = a(n-8) = a(n-1) - a(n-4) + a(n-5).
G.f.: -x*(1+x^3-x)/((x-1)*(1+x^4)). (End)
a(n) = (1-(-1)^((n+5)*(n+6)*(n^2+11*n+32)/8))/2. - Wesley Ivan Hurt, Aug 23 2015
a(n) = A165211(n+5). - Wesley Ivan Hurt, Aug 23 2015
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MAPLE
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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
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MATHEMATICA
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CoefficientList[Series[x*(1 - x + x^3)/((1 - x)*(1 + x^4)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 23 2015 *)
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PROG
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(PARI) a(n)=((n%8>3)+(n%4==1))%2 \\ Jaume Oliver Lafont, Mar 19 2009]
(PARI) a(n)=210\2^(n%8)%2; \\ Jaume Oliver Lafont, Mar 24 2009]
(PARI) apply( A130198(n)=bittest(210, n%8), [0..99]) \\ M. F. Hasler, May 24 2019
(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
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CROSSREFS
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Cf. A121262, A131078. - Jaume Oliver Lafont, Mar 19 2009
Cf. A165211.
Sequence in context: A282244 A286691 A288462 * A285411 A104893 A104894
Adjacent sequences: A130195 A130196 A130197 * A130199 A130200 A130201
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KEYWORD
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nonn,easy
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AUTHOR
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Simone Severini, May 16 2007
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STATUS
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approved
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