A382910 a(n) = A003266(n)^2.

1, 1, 1, 4, 36, 900, 57600, 9734400, 4292870400, 4962558182400, 15011738501760000, 118907980672440960000, 2465675887223735746560000, 133859078241489389944995840000, 19025256931384645503492313743360000, 7079298104168226591849489943904256000000, 6896432754839457130755425769163265163264000000

Offset

0,4

Comments

For n>=3 number of valid symmetrical change ringing methods on n bells with the shortest number of rows per lead where the treble plain hunts out to the back. See Wikipedia and the Polster and Ross link for an explanation of bell ringing terminology.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..70

Richard Duckworth and Fabian Stedman, Tintinnalogia, or, the Art of Ringing, (1671). Released by Project Gutenberg, 2006.

Burkard Polster and Marty Ross, Ringing the changes, (2009).

Wikipedia, Method ringing.

Index entries for sequences related to bell ringing.

Formula

a(n) = Product_{j=1..n} Fibonacci(j)^2.

a(0) = 1; a(n) = a(n-1)*A007598(n). - Hugo Pfoertner, Apr 13 2025

a(n) ~ c^2 * phi^(n*(n+1)) / 5^n where phi is the golden ratio (A001622) and c = A062073. - Amiram Eldar, Aug 18 2025

Maple

a:= proc(n) a(n):= `if`(n=0, 1, a(n-1)*(<<0|1>, <1|1>>^n)[1, 2]^2) end:
seq(a(n), n=0..16);  # Alois P. Heinz, Apr 14 2025

Mathematica

k = 1; {1, 1}~Join~Reap[Do[k *= Fibonacci[n]; Sow[k^2], {n, 16}] ][[-1, 1]] (* Michael De Vlieger, Apr 14 2025 *)

Crossrefs

Cf. A000045, A001622, A003266, A007598, A062073, A090281.

Sequence in context: A134052 A127901 A061742 * A136469 A120605 A337851

Adjacent sequences: A382907 A382908 A382909 * A382911 A382912 A382913

Keyword

nonn,easy

Author

Edwin Hermann, Apr 08 2025

Status

approved