OFFSET
0,2
COMMENTS
If w is a binary string of length 2n-1 and v(w) is a vector of the Hamming weights of each substring of length n, then a(n) is the number of distinct v(w) for all possible w. - Orson R. L. Peters, Jun 01 2017
REFERENCES
S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-9).
FORMULA
G.f.: (1-2*x)^2/(1-3*x)^2. [Detlef Pauly (dettodet(AT)yahoo.de), Mar 03 2003]
a(n) = 6*a(n-1)-9*a(n-2) for n>2. a(n) = 3^(n-2)*(n+5) for n>0. [Colin Barker, Jun 25 2012]
MAPLE
seq(ceil(1/9*3^n*(5+n)), n=0..50);
MATHEMATICA
CoefficientList[Series[(1 - 2 x)^2/(1 - 3 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{6, -9}, {1, 2, 7}, 30] (* Harvey P. Dale, Jul 04 2018 *)
PROG
(Magma) [1] cat [3^(n-2)*(n+5): n in [1..30]]; // Vincenzo Librandi, Oct 22 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 03 2000
EXTENSIONS
More terms from James A. Sellers, May 03 2000
STATUS
approved