OFFSET
1,4
COMMENTS
a(n) is also the number of 5 boxes polyomino (invert U patterns) packing into n X n square. The 6 boxes 2 X 3 (rectangular patterns) also gives the same sequence but difference in squares left. See illustration in links. - Kival Ngaokrajang, Nov 10 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Kival Ngaokrajang, Illustration of initial terms of invert u and 2 X 3 rectangular patterns.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1,1,0,-1,-1,0,1).
FORMULA
a(n) = a(n-2) + a(n-3) - a(n-5) + a(n-6) - a(n-8) - a(n-9) + a(n-11). - Clark Kimberling, May 18 2012
G.f.: -x^3*(x^7+x^6+x^5+2*x^4+3*x^3+x^2+2*x+1) / ((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+x+1)^2). - Colin Barker, Apr 05 2013
Sum_{n>=3} (-1)^(n+1)/a(n) = sqrt(3)*Pi/4 + 9*log(3)/4 - 2*log(2) - 3/2. - Amiram Eldar, Mar 30 2023
MAPLE
[ seq(floor(n/2)*floor(n/3), n=1..64) ];
MATHEMATICA
Table[Floor[n/2]*Floor[n/3], {n, 1, 70}] (* Clark Kimberling, May 18 2012 *)
CoefficientList[Series[- x^2 x^7 + x^6 + x^5 + 2 x^4 + 3 x^3 + x^2 + 2 x+1)/((x - 1)^3 (x + 1)^2 (x^2 - x + 1) (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 1}, {0, 0, 1, 2, 2, 6, 6, 8, 12, 15, 15}, 60] (* Harvey P. Dale, Jan 09 2016 *)
PROG
(Magma) [Floor(n/2)*Floor(n/3) : n in [1..50]]; // Wesley Ivan Hurt, Jun 22 2014
(PARI) a(n)=n\2 + n\3 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved