

A026097


a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, s(i)  s(i1) = 1 for i = 1,2,3; s(i)  s(i1) <= 1 for i >= 4. Also a(n) = sum of numbers in row n+1 of the array T defined in A026082 and a(n) = 24*3^(n4) for n >= 4.


2



1, 2, 4, 8, 24, 72, 216, 648, 1944, 5832, 17496, 52488, 157464, 472392, 1417176, 4251528, 12754584, 38263752, 114791256, 344373768, 1033121304, 3099363912, 9298091736, 27894275208, 83682825624, 251048476872, 753145430616, 2259436291848
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Also length of successive strings generated by an alternating Kolakoski (2,4) rule starting at 4 (i.e. string begins with 2 if previous string ends with 4 and vice et versa) : 4>2222>44224422>444422224422444422224422>... and length of strings are 1,4,8,24,72,...  Benoit Cloitre, Oct 15 2005


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3).


FORMULA

a(n) = 3*a(n1) for n>3. G.f.: (4*x^3+2*x^2+x1) / (3*x1).  Colin Barker, Jun 15 2013


MATHEMATICA

CoefficientList[Series[(4 x^3 + 2 x^2 + x  1)/(3 x  1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 18 2013 *)


CROSSREFS

Essentially the same as A005051.
Sequence in context: A114900 A264570 A115115 * A264557 A067646 A152875
Adjacent sequences: A026094 A026095 A026096 * A026098 A026099 A026100


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling


STATUS

approved



