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 A010762 a(n) = floor( n/2 ) * floor( n/3 ). 8
 0, 0, 1, 2, 2, 6, 6, 8, 12, 15, 15, 24, 24, 28, 35, 40, 40, 54, 54, 60, 70, 77, 77, 96, 96, 104, 117, 126, 126, 150, 150, 160, 176, 187, 187, 216, 216, 228, 247, 260, 260, 294, 294, 308, 330, 345, 345, 384, 384, 400, 425, 442, 442, 486, 486, 504, 532, 551 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = A004526(n) * A002264(n). - Reinhard Zumkeller, Jul 25 2005 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 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 Cf. A010761, A110533, A242669. Sequence in context: A267516 A163118 A319010 * A055993 A309912 A222734 Adjacent sequences:  A010759 A010760 A010761 * A010763 A010764 A010765 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)