A060495 Each permutation in the list A060117 converted to Site Swap notation, with "zero throws" (fixed elements) replaced with n, the length of siteswap.

1, 11, 312, 111, 231, 222, 4413, 1313, 4112, 1111, 2411, 2312, 4242, 1241, 4233, 1223, 2222, 2231, 3441, 3342, 3131, 3122, 3423, 3333, 55514, 14514, 51414, 11314, 25314, 24414, 55113, 14113, 51112, 11111, 25111, 24112, 52512, 12511, 52413

Offset

0,2

Comments

This sequence is not well-defined for n >= 3628800 because the Site Swap notation can contain values exceeding 9, for example, the Site Swap notation for a(3628800) is [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10]. - Sean A. Irvine, Nov 25 2022

Links

Table of n, a(n) for n=0..38.

Site Swap notation explained.

Formula

a(n) = SiteSwap1ToDec(Perm2SiteSwap1(PermUnrank3R(n))).

Maple

Perm2SiteSwap1 := proc(p) local ip, n, i, a; n := nops(p); ip := convert(invperm(convert(p, 'disjcyc')), 'permlist', n); a := []; for i from 1 to n do a := [op(a), ((ip[i]-i) mod n)]; od; RETURN(a); end;
SiteSwap1ToDec := proc(s) local i, z, n; n := nops(s); z := 0; for i from 1 to n do z := 10*z; if(0 = s[i]) then z := z+n; else z := z+s[i]; fi; od; RETURN(z); end;

Crossrefs

Cf. factorial base representation A007623 and A060496, A006694.

See also A060498, A060499, A061417. Average of digits gives number of balls: A060501.

Sequence in context: A193890 A317744 A185071 * A251589 A070278 A090272

Adjacent sequences: A060492 A060493 A060494 * A060496 A060497 A060498

Keyword

nonn,base

Author

Antti Karttunen, Mar 21 2001

Status

approved