A090284 "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 4 (the tenor bell) in n-th permutation.

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

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

Index entries for periodic sequences.

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

Mathematica

CoefficientList[Series[x (-3x^20-x^19+x^17-2x^16-2x^12+x^11-x^9-3x^8-4x^4+x^3+x^2+x-4)/((x-1)(x^4+1)(x^2-x+1)(x^2+x+1)(x^4-x^2+1)(x^8-x^4+1)), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1}, {4, 3, 2, 1, 1, 2, 3, 4, 3, 4, 4, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3}, 100] (* Harvey P. Dale, Mar 29 2026 *)

Prog

(PARI) a(n)=58866464597535348\5^(n%24)%5 \\ Charles R Greathouse IV, May 15 2026

Crossrefs

Cf. A090277-A090283.

Sequence in context: A070635 A110366 A284801 * A369110 A369826 A093580

Adjacent sequences: A090281 A090282 A090283 * A090285 A090286 A090287

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 24 2004

Status

approved