OFFSET
1,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
J.-J. Bode, H. Harborth and M. Harborth, King independence on triangle boards, Discr. Math., 266 (2003), 101-107.
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,0,1,-2,1).
FORMULA
a(n) = floor((n+1)^2/4) if n == 0, 1, 4, 6, 9, 10, 11 (mod 12), a(n) = floor((n+1)^2/4) - 1 otherwise.
a(n)= +2*a(n-1) -a(n-2) +a(n-12) -2*a(n-13) +a(n-14). - R. J. Mathar, Aug 05 2014
G.f.: -x*(1-x+2*x^2-x^4+2*x^5-x^6+x^7+2*x^8-x^9+x^10+x^3) / ( (1+x) *(1+x^2) *(x^4-x^2+1) *(x^2-x+1) *(1+x+x^2) *(x-1)^3 ). - R. J. Mathar, Aug 05 2014
MATHEMATICA
CoefficientList[Series[-(1 - x + 2 x^2 - x^4 + 2 x^5 - x^6 + x^7 + 2 x^8 - x^9 + x^10 + x^3)/((1 + x) (1 + x^2) (x^4 - x^2 + 1) (x^2 - x + 1) (1 + x + x^2) (x - 1)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 06 2014 *)
PROG
(Magma) I:=[1, 1, 3, 6, 8, 12, 15, 19, 25, 30, 36, 42, 49, 55]; [n le 14 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-12)-2*Self(n-13)+Self(n-14): n in [1..60]]; // Vincenzo Librandi, Aug 06 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 25 2003
EXTENSIONS
More terms from Sean A. Irvine, Sep 26 2011
STATUS
approved