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
KEYWORD
easy,nonn
AUTHOR
R. Tonelli (roberto.tonelli(AT)dsf.unica.it), Aug 31 2007
STATUS
approved