OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
J.-P. Bode and H. Harborth, Independence for knights on hexagon and triangle boards, Discrete Math., 272 (2003), 27-35.
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,0,-1,2,0,-2,1).
FORMULA
a(n) = ceiling(n^2/4) if n == 0, 1, 4, 8, 11 (mod 12), ceiling(n^2/4) + 1 if n == 3, 9 (mod 12) and ceiling(n^2/4) + 2 if n == 2, 5, 6, 7, 10 (mod 12) and n != 6.
G.f.: x*(1+x-2*x^2-2*x^3+6*x^4-x^5-4*x^6+x^7+3*x^8-x^9+x^11-2*x^12+2*x^14-x^15) / ((1-x)^3*(1+x)*(1+x^2)*(1-x^2+x^4)). - Colin Barker, Feb 02 2016
PROG
(PARI) Vec(x*(1+x-2*x^2-2*x^3+6*x^4-x^5-4*x^6+x^7+3*x^8-x^9+x^11-2*x^12+2*x^14-x^15)/((1-x)^3*(1+x)*(1+x^2)*(1-x^2+x^4)) + O(x^100)) \\ Colin Barker, Feb 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 21 2003
EXTENSIONS
More terms from David Wasserman, May 06 2005
STATUS
approved