A131601 The 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 an block of length at least m made of first symbol. Here k=49 and m=2.

49, 97, 145, 2497, 7153, 14113, 133969, 477313, 1154737, 7585249, 30496273, 85923649, 450015601, 1913836705, 6038171857, 27638920705, 119503082545, 409335331681, 1736003525521, 7472151487681, 27120247408369, 110448416633377, 469111688042065, 1770883563643777

Offset

1,1

Comments

For k=2 is the number of different configurations of an n-bits string where each 1 is isolated and separated by at least m zeros.

Limit as n-> infinity (a(n+1)/a(n)) -> 4.

Links

Table of n, a(n) for n=1..24.

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, 48).

Formula

a(n) = a(n-1) + (k-1)*a(n-m-1), where k=49, m=2, n>=4, with a(1) = 49, a(2) = 97, a(3) = 145.

G.f.: -x*(49+48*x+48*x^2)/(4*x-1)/(12*x^2+3*x+1). - R. J. Mathar, Nov 14 2007

Mathematica

Rest[CoefficientList[Series[-x*(49+48*x+48*x^2)/(4*x-1)/(12*x^2+3*x+1), {x, 0, 50}], x]] (* G. C. Greubel, May 02 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(-x*(49+48*x+48*x^2)/(4*x-1)/(12*x^2+3*x+1)) \\ G. C. Greubel, May 02 2017

Crossrefs

Cf. A000045, A000930, A131600.

Sequence in context: A043250 A044030 A165339 * A309541 A174386 A044138

Adjacent sequences: A131598 A131599 A131600 * A131602 A131603 A131604

Keyword

easy,nonn

Author

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

Status

approved