A130198 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.

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

Offset

0,1

Comments

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

Links

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).

Formula

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

Maple

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

Mathematica

CoefficientList[Series[x*(1 - x + x^3)/((1 - x)*(1 + x^4)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 23 2015 *)

Prog

(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

Crossrefs

Cf. A121262, A131078. - Jaume Oliver Lafont, Mar 19 2009

Cf. A165211.

Sequence in context: A359172 A288462 A361460 * A285411 A104893 A104894

Adjacent sequences: A130195 A130196 A130197 * A130199 A130200 A130201

Keyword

nonn,easy

Author

Simone Severini, May 16 2007

Status

approved