A090282 "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 2 in n-th permutation.

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

Offset: 1

Author

N. J. A. Sloane, Jan 24 2004

Keywords

• nonn

Links

• 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

Crossrefs

Cf. A090277-A090284.

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*(-2*x^20 + x^19 - x^17 - 3*x^16 - 4*x^12 + x^11 + x^10 + x^9 - 4*x^8 - 3*x^4 - x^3 + x - 2)/((x - 1)*(x^4 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^8 - x^4 + 1)). (End)