The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Herbert Kociemba (See also Herbert Kociemba's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A333298

Number of canonical sequences of moves of length n for the Rubik cube puzzle using the half-turn metric.
(history; published version)

#16 by Herbert Kociemba at Sat Feb 17 08:13:04 EST 2024

STATUS

editing

proposed

#15 by Herbert Kociemba at Sat Feb 17 07:33:05 EST 2024

FORMULA

Conjectures from _From _Colin Barker_, Mar 23 2020: (Start)

STATUS

approved

editing

Discussion

Sat Feb 17

08:09

Herbert Kociemba: The conjectures from Colin Barker are definitely true. In the outer block turn metric (OBTM) for N x N x N Rubik's Cubes I derived years ago a astonishing simple generating function for the number of canonical sequences
3/(6 - 4 (3 x + 1)^(n - 1)) - 1/2

and Colin's  formulas result from the case n=3.
For n=2 we get for example corresponding formulas
G.f.: (1+3 x)/(1-6 x)
a(n) = 6*a(n-1) for n>1
a(n)=2^(-1+n) 3^(1+n)

and for n=4
G.f: -(1/2)+3/(6-4 (1+3 x)^3)
a(n)=18*a(n-1)+54*a(n-2)+54*a(n-3) for n>3

A080656

Order of group of n X n X n Rubik cube, under assumptions not-s, m, not-i.
(history; published version)

#14 by Herbert Kociemba at Sun Jul 03 20:27:39 EDT 2022

STATUS

editing

proposed

#13 by Herbert Kociemba at Sun Jul 03 20:27:15 EDT 2022

MATHEMATICA

f[1]=1; f[2]=7!3^6; f[3]=8!3^7 12!2^10; f[n_]:=f[n-2]*24!(24!/2)^(n-3); Table Array[f[n], {n, 1, 10}, 5] (* _Herbert Kociemba_, Dec 08 2016 *)

(* Herbert Kociemba, Dec 08 2016 *)

f[1]=1; f[n_]:=7!3^6(6*24!!)^(s=Mod[n, 2])24!^(r=(n-s)/2-1) (24!/2)^(r(r+s)); Array[f, 5] (* _Herbert Kociemba_, Jul 03 2022 *)

(* Herbert Kociemba, Jul 03 2022 *)

#12 by Herbert Kociemba at Sun Jul 03 20:19:00 EDT 2022

MATHEMATICA

f[1]=1; f[n_]:=7!3^6(6*24!!)^(s=Mod[n, 2])24!^(r=(n-s)/2-1) (24!/2)^(r(r+s)); Array[f, 5] (* Herbert Kociemba, Jul 03 2022 *)

STATUS

approved

editing

A075152

Number of possible permutations of a Rubik cube of size n X n X n.
(history; published version)

#75 by Herbert Kociemba at Sun Jul 03 19:01:10 EDT 2022

STATUS

editing

proposed

#74 by Herbert Kociemba at Sun Jul 03 19:00:22 EDT 2022

MATHEMATICA

f[1]=1; f[n_]:=7!3^6(6*24!!)^(s=Mod[n, 2])24!^(r=(n-s)/2-1)(24!/4!^6)^(r(r+s)) ; Array[f, 5] (*Herbert Kociemba, Jul 03 2022*)

#73 by Herbert Kociemba at Sun Jul 03 18:58:32 EDT 2022

MATHEMATICA

f[1]=1; f[n_]:=7!3^6(36*1224!!*2^13)^(s=Mod[n, 2])24!^(r=(n-s)/2-1)(24!/4!^6)^(r(r+s)); Table Array[f[n], {n, 1, 10}, 5] (* _Herbert Kociemba_, , Jul 03 2022 *)

STATUS

proposed

editing

#72 by Herbert Kociemba at Sun Jul 03 16:52:14 EDT 2022

STATUS

editing

proposed

#71 by Herbert Kociemba at Sun Jul 03 16:50:47 EDT 2022

MATHEMATICA

f[1]=1; f[n_]:=7!3^6(3*12!*2^13)^(s=Mod[n, 2])24!^(r=(n-s)/2-1)(24!/4!^6)^(r^2(r+s*r)); Table[f[n], {n, 1, 10}] (* Herbert Kociemba, Jul 03 2022 *)

STATUS

proposed

editing

Discussion

Sun Jul 03

16:52

Herbert Kociemba: Hope it is not too annoying to propose several times within short intervals.