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A131600
Number of different configurations of an n-block of a shift space with k symbols where each symbol but the first must appear isolated and separated from others by a block of length at least m made of first symbols. Here k=19 and m=2.
2
19, 37, 55, 397, 1063, 2053, 9199, 28333, 65287, 230869, 740863, 1916029, 6071671, 19407205, 53895727, 163185805, 512515495, 1482638581, 4419983071, 13645261981, 40332756439, 119892451717, 365507167375, 1091496783277, 3249560914183, 9828689926933, 29475632025919
OFFSET
1,1
COMMENTS
For k=2 is the number of different configurations of an n-bit string where each 1 is isolated and separated by at least m zeros.
Limit as n-> infinity (a(n+1)/a(n)) -> 3.
FORMULA
a(n) = a(n-1) + (k-1)*a(n-m-1), where k=19, m=2.
G.f.: -x*(19+18*x+18*x^2)/(3*x-1)/(6*x^2+2*x+1). - R. J. Mathar, Nov 14 2007
MATHEMATICA
Rest[CoefficientList[Series[-x*(19 + 18*x + 18*x^2)/(3*x - 1)/(6*x^2 + 2*x + 1), {x, 0, 50}], x]] (* G. C. Greubel, May 02 2017 *)
PROG
(PARI) x='x+O('x^50); Vec(-x*(19+18*x+18*x^2)/(3*x-1)/(6*x^2+2*x+1)) \\ G. C. Greubel, May 02 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
R. Tonelli (roberto.tonelli(AT)dsf.unica.it), Aug 31 2007
STATUS
approved