OFFSET
0,14
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: x^12/((x^11+x-1)*(x^12+x-1)).
a(n) = 2*a(n-1) -a(n-2) +a(n-11) -a(n-13) -a(n-23). - Vincenzo Librandi, Jun 05 2013
EXAMPLE
a(13)=2 because 2 binary words of length 13 have at least one subword 10^{10}1 and no subwords 10^{i}1 with i<10: 0100000000001, 1000000000010.
MAPLE
a:= n-> coeff(series(x^12/((x^11+x-1)*(x^12+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);
MATHEMATICA
CoefficientList[Series[x^12 / ((x^11 + x - 1) (x^12 + x - 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 05 2013 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, 80] (* Harvey P. Dale, Aug 20 2021 *)
PROG
(Magma) [n le 12 select 0 else n le 23 select n-12 else 2*Self(n-1)-Self(n-2) +Self(n-11)-Self(n-13)-Self(n-23): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 04 2008
STATUS
approved