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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
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 (list; graph; refs; listen; history; text; internal format)
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: A234361 A240450 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

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Last modified May 25 16:08 EDT 2020. Contains 334594 sequences. (Running on oeis4.)