A133926 Number of equivalence classes of compositions of n into parts of size 2 and 3 under the following equivalence relation: We make a "move" by changing three consecutive 2s into two consecutive 3s or vice versa. Two compositions are equivalent if we can reach one from the other by a series of moves.

1, 0, 1, 1, 1, 2, 1, 3, 2, 3, 4, 3, 6, 4, 7, 7, 7, 11, 8, 14, 12, 15, 19, 16, 26, 21, 30, 32, 32, 46, 38, 57, 54, 63, 79, 71, 104, 93, 121, 134, 135, 184, 165, 226, 228, 257, 319, 301, 411, 394, 484, 548, 559, 731, 696, 896, 943, 1044, 1280, 1256, 1628, 1640, 1941, 2224, 2301, 2909

Offset

0,6

Comments

Sequence A133925 counts the equivalence classes with exactly one element.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Problem posed on the Art of Problem Solving forum, String Replacement

Formula

a(n) = a(n-2) + a(n-3) - a(n-6). - Franklin T. Adams-Watters, Oct 12 2013

G.f.: 1/(1-x^2-x^3+x^6). [Joerg Arndt, Oct 12 2013]

Example

a(5) = 2 because the two compositions 23 and 32 are inequivalent. a(6) = 1 because the two compositions 222 and 33 are equivalent.

Mathematica

a=b=c=d=e=0; Delete[Table[z=a+b+c-e+1; a=b; b=c; c=d; d=e; e=z, {n, 100}], {{1}, {2}}] (* Vladimir Joseph Stephan Orlovsky, Feb 27 2011 *)

Prog

(PARI) Vec( 1/(1-x^2-x^3+x^6) +O(x^66) ) \\ Joerg Arndt, Oct 12 2013

Crossrefs

Sequence in context: A352129 A340351 A115872 * A144337 A143929 A153583

Adjacent sequences: A133923 A133924 A133925 * A133927 A133928 A133929

Keyword

easy,nonn

Author

Joel B. Lewis, Jan 07 2008, Jan 23 2008

Extensions

More terms from Joerg Arndt, Oct 12 2013

Status

approved