A090283 "Plain Bob Minimus" in bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 3 in n-th permutation.

3, 4, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 4, 3, 4, 3, 2, 1, 1, 2, 3, 4, 3, 4, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 4, 3, 4, 3, 2, 1, 1, 2, 3, 4, 3, 4, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 4, 3, 4, 3, 2, 1, 1, 2, 3, 4, 3, 4, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 4, 4, 3, 4, 3, 2, 1, 1, 2, 3, 4, 3, 4, 4

Offset

1,1

Links

Table of n, a(n) for n=1..99.

David Joyner, Application: Bell Ringing

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1).

Index entries for sequences related to bell ringing

Formula

Period 24.

From Chai Wah Wu, Jul 17 2016: (Start)

a(n) = a(n-1) - a(n-4) + a(n-5) - a(n-8) + a(n-9) - a(n-12) + a(n-13) - a(n-16) + a(n-17) - a(n-20) + a(n-21) for n > 21.

G.f.: x*(-4*x^20 + x^19 + x^18 + x^17 - 4*x^16 - 3*x^12 - x^11 + x^9 - 2*x^8 - 2*x^4 + x^3 - x - 3)/((x - 1)*(x^4 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^8 - x^4 + 1)). (End)

Crossrefs

Cf. A090277-A090284.

Sequence in context: A105736 A248158 A360268 * A318705 A334492 A306571

Adjacent sequences: A090280 A090281 A090282 * A090284 A090285 A090286

Keyword

nonn

Author

N. J. A. Sloane, Jan 24 2004

Status

approved