OFFSET
0,2
COMMENTS
All terms with index n > 0 are even.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..4193
Index entries for linear recurrences with constant coefficients, signature (0,8,0,-22,0,23,0,-6).
FORMULA
G.f.: -(x+1)*(4*x^7-4*x^6-7*x^5-5*x^4+5*x^3+5*x^2-x-1) / ((3*x^2-1) *(2*x^2-1) *(x^2+x-1) *(x^2-x-1)).
a(n) <= A306306(n).
EXAMPLE
a(3) = 6: 001, 010, 011, 100, 101, 110.
a(4) = 10: 0010, 0011, 0100, 0101, 0110, 1001, 1010, 1011, 1100, 1101.
a(5) = 16: 00101, 00110, 01001, 01010, 01011, 01100, 01101, 01110, 10001, 10010, 10011, 10100, 10101, 10110, 11001, 11010.
a(6) = 26: 001010, 001011, 001100, 001101, 001110, 010010, 010011, 010100, 010101, 010110, 011001, 011010, 011100, 100011, 100101, 100110, 101001, 101010, 101011, 101100, 101101, 110001, 110010, 110011, 110100, 110101.
a(7) = 42: 0010101, 0010110, 0011001, ..., 1100110, 1101001, 1101010.
a(8) = 70: 00101010, ..., 00111100, ..., 11000011, ..., 11010101.
MAPLE
a:= n-> `if`(n<2, 1+n, 2*(<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>,
<-6|23|-22|8>>^iquo(n-2, 2, 'r').[<<2, 5, 13, 35>>,
<<3, 8, 21, 55>>][1+r])[1, 1]):
seq(a(n), n=0..50);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Feb 04 2019
STATUS
approved