OFFSET
1,1
COMMENTS
Row 2 of A228660.
The recurrence is demonstrated as follows: For every 2X(n-1) array, we can add the column (0,0) to get an appropriate array of size 2Xn, and for every 2X(n-2) array, we can add the column (0,0) and either (1,0), (0,1) or (1,1) to get an appropriate sized array. Every admissible array is of one of these two forms, and these two forms do not overlap (since their last columns are different). - Tom Edgar, Aug 29 2013
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Index entries for linear recurrences with constant coefficients, signature (1,3).
FORMULA
a(n) = a(n-1) +3*a(n-2).
G.f.: -2*x / ( -1+x+3*x^2 ). a(n) = 2*A006130(n-1). - R. J. Mathar, Aug 29 2013
a(n) = -2/13*sqrt(13)*(-1/2*sqrt(13)+1/2)^n + 2/13*sqrt(13)*(1/2*sqrt(13)+1/2)^n. - Tom Edgar, Aug 31 2013
G.f.: Q(0)/x -1/x, where Q(k) = 1 + 3*x^2 + (2*k+3)*x - x*(2*k+1 + 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013
EXAMPLE
Some solutions for n=4
..1..0..1..0....1..0..0..0....1..0..0..1....1..0..0..0....1..0..1..0
..1..0..1..0....1..0..0..0....1..0..0..0....0..0..1..0....0..0..0..0
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 29 2013
STATUS
approved