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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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

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: A282244 A286691 A288462 * A285411 A104893 A104894

Adjacent sequences:  A130195 A130196 A130197 * A130199 A130200 A130201

KEYWORD

nonn,easy

AUTHOR

Simone Severini, May 16 2007

STATUS

approved

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Last modified May 28 13:05 EDT 2022. Contains 354115 sequences. (Running on oeis4.)