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A213032
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a(n) = floor(n/2)*floor(n/3)-floor(n/6)^2.
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2
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0, 0, 0, 1, 2, 2, 5, 5, 7, 11, 14, 14, 20, 20, 24, 31, 36, 36, 45, 45, 51, 61, 68, 68, 80, 80, 88, 101, 110, 110, 125, 125, 135, 151, 162, 162, 180, 180, 192, 211, 224, 224, 245, 245, 259, 281, 296, 296, 320, 320, 336, 361, 378, 378, 405, 405, 423, 451
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OFFSET
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0,5
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,2,-2,0,0,0,0,-1,1).
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FORMULA
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a(n) = a(n-1)+2*a(n-6)-2*a(n-7)-a(n-12)+a(n-13).
G.f.: (x^3 + x^4 + 3*x^6 + 2*x^8 + 2*x^9 + x^10)/(1 - x - 2*x^6 + 2*x^7 + x^12 - x^13).
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MATHEMATICA
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a[n_] := Floor[n/2]*Floor[n/3] - Floor[n/6]^2
Table[a[n], {n, 0, 90}] (* A213032 *)
LinearRecurrence[{1, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -1, 1}, {0, 0, 0, 1, 2, 2, 5, 5, 7, 11, 14, 14, 20}, 90]
CoefficientList[Series[(x^3 + x^4 + 3 x^6 + 2 x^8 + 2 x^9 + x^10) / (1 - x - 2 x^6 + 2 x^7 + x^12 - x^13), {x, 0, 80}], x] (* Vincenzo Librandi, Aug 02 2013 *)
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PROG
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(Magma) [Floor(n/2)*Floor(n/3)-Floor(n/6)^2: n in [0..80]]; // Vincenzo Librandi, Aug 02 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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