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.

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.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

R. Tonelli, Fibonacci-like sequences and shift spaces in symbolic dynamics, arXiv:0708.4370, [math.DS], 2007.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 18).

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

Cf. A000045, A000930, A131601.

Sequence in context: A225863 A332884 A161705 * A175546 A162471 A124268

Adjacent sequences: A131597 A131598 A131599 * A131601 A131602 A131603

Keyword

easy,nonn

Author

R. Tonelli (roberto.tonelli(AT)dsf.unica.it), Aug 31 2007

Status

approved