OFFSET
0,6
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,3,2).
FORMULA
G.f.: x^4/((1 - 2*x)*(1 - x - x^2)^2).
a(n) -2*a(n-1) = A001629(n-2). - R. J. Mathar, May 06 2016
EXAMPLE
a(5) = 4 because we have: 00011, 00110, 00111, 10011.
We also note that words such as 001011 are included in this enumeration because the pair of consecutive 1's need not immediately follow the pair of consecutive 0's.
MATHEMATICA
nn=30; r=Solve[{s==1+x a+x s, a==x s, b==x a+x b+x c, c==x b, d==x c + 2x d}, {s, a, b, c, d}]; CoefficientList[Series[d/.r, {x, 0, nn}], x]
CoefficientList[ Series[ x^4/((1 - 2x)(1 - x - x^2)^2), {x, 0, 34}], x] (* Robert G. Wilson v, Feb 01 2015 *)
LinearRecurrence[{4, -3, -4, 3, 2}, {0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Jun 23 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Geoffrey Critzer, Jan 18 2014
STATUS
approved