A244044 Number of length n words on alphabet {0,1,2,3} which contain all 16 of the 2-letter strings of the alphabet.

331776, 5806080, 69672960, 675578880, 5675235840, 42832800000, 297267224832, 1927826369280, 11821052680704, 69152452363584, 388663047288576, 2110540207741632, 11123834480487936, 57120835559901696, 286669843226634240, 1409843999618778240, 6809949521252980992

Offset

17,1

Comments

The expected wait time to see all 16 2-letter subwords is: 3401981586663184695807274256173879732908913569174615510479814304735002007 *1982900192550576041 / (2^3 *3^3 *5^3 *11^2 *13^2 *17 *19 *23 *29 *31 *37 *41 *43 *47 *53 *59 *61 *67 *71 *73 *79 *83 *89 *97 *101 *103 *107 *113 *127 *131 *137 *139 *149 *151 *157 *163 *167 *173 *179 *191 *199 *211 *223 *227 *239 *251) (approximately 55.0688).

Links

Alois P. Heinz, Table of n, a(n) for n = 17..150

Maple

b:= proc(n, t, s) option remember; `if`(s={}, 4^n, `if`(nops(s)>n,
       0, add(b(n-1, j, s minus {4*t+j}), j=0..3)))
    end:
a:= n-> 4*b(n-1, 0, {$0..15}):
seq(a(n), n=17..25);  # Alois P. Heinz, Jun 18 2014

Mathematica

abcd=Solve[{aa==uaa(z^2+z(aa+ab+ac+ad)), ab==uab(z^2+z(ba+bb+bc+bd)), ac==uac(z^2+z(ca+cb+cc+cd)), ad==uad(z^2+z(da+db+dc+dd)), ba==uba(z^2+z(aa+ab+ac+ad)), bb==ubb(z^2+z(ba+bb+bc+bd)), bc==ubc(z^2+z(ca+cb+cc+cd)), bd==ubd(z^2+z(da+db+dc+dd)), ca==uca(z^2+z(aa+ab+ac+ad)), cb==ucb(z^2+z(ba+bb+bc+bd)), cc==ucc(z^2+z(ca+cb+cc+cd)), cd==ucd(z^2+z(da+db+dc+dd)), da==uda(z^2+z(aa+ab+ac+ad)), db==udb(z^2+z(ba+bb+bc+bd)), dc==udc(z^2+z(ca+cb+cc+cd)), dd==udd(z^2+z(da+db+dc+dd))}, {aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd}];
fz[uaa_, uab_, uac_, uad_, uba_, ubb_, ubc_, ubd_, uca_, ucb_, ucc_, ucd_, uda_, udb_, udc_, udd_] =aa+ab+ac+ad+ba+bb+bc+bd+ca+cb+cc+cd+da+db+dc+dd/.abcd//Simplify;
t=Map[Total[Map[Apply[fz, #]&, #]]&, Table[Select[Tuples[{0, 1}, 16], Count[#, 0]==n&], {n, 0, 16}]];
nn=35; Drop[Flatten[CoefficientList[Series[Sum[(-1)^(i+1)t[[i]], {i, 1, 16}], {z, 0, nn}], z]], 17]

Crossrefs

Cf. A243862.

Sequence in context: A259011 A259004 A256902 * A134359 A013913 A258897

Adjacent sequences: A244041 A244042 A244043 * A244045 A244046 A244047

Keyword

nonn

Author

Edward Williams and Geoffrey Critzer, Jun 17 2014

Status

approved