

A101169


Lengths of successive words (starting with a) under the substitution: {a > aab, b > aac, c > ab}.


1



1, 3, 9, 26, 76, 221, 644, 1875, 5461, 15903, 46314, 134876, 392791, 1143896, 3331289, 9701475, 28252921, 82278978, 239615244, 697814501, 2032195756, 5918219771, 17235212309, 50192888175, 146173193506, 425689839228
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OFFSET

0,2


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 3, 1).


FORMULA

a(n) = 2*a(n1) + 3*a(n2)  a(n3).
G.f.: (x+1) / (x^3+3*x^2+2*x1).


EXAMPLE

a => aab => aabaabaac => aabaabaacaabaabaacaabaabab, thus a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 26.


MAPLE

a:= n> (<<010>, <001>, <132>>^n. <<0, 1, 3>>)[2, 1]:
seq(a(n), n=0..30); # Alois P. Heinz, May 06 2011


MATHEMATICA

LinearRecurrence[{2, 3, 1}, {1, 3, 9}, 40] (* Harvey P. Dale, Feb 19 2012 *)


CROSSREFS

Cf. A101399, A101400.
Sequence in context: A123941 A005774 A273343 * A119826 A027915 A295115
Adjacent sequences: A101166 A101167 A101168 * A101170 A101171 A101172


KEYWORD

easy,nonn


AUTHOR

Jeroen F.J. Laros, Jan 22 2005


EXTENSIONS

Terms >=1875 by Alois P. Heinz, May 06 2011


STATUS

approved



