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URL: https://oeis.org/A213029

⇱ A213029 - OEIS

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A213029
a(n) = floor(n/2)^2 - floor(n/3)^2.
1
0, 0, 1, 0, 3, 3, 5, 5, 12, 7, 16, 16, 20, 20, 33, 24, 39, 39, 45, 45, 64, 51, 72, 72, 80, 80, 105, 88, 115, 115, 125, 125, 156, 135, 168, 168, 180, 180, 217, 192, 231, 231, 245, 245, 288, 259, 304, 304, 320, 320, 369, 336, 387, 387, 405, 405, 460, 423
OFFSET
0,5
LINKS
FORMULA
a(n) = -a(n-1)+a(n-2)+3*a(n-3)+2*a(n-4)-2*a(n-5)-3*a(n-6)-a(n-7)+a(n-8)+a(n-9).
G.f.: (x^2 + x^3 + 2*x^4 + 3*x^5 + 3*x^6)/(1 + x - x^2 - 3 x^3 - 2*x^4 + 2*x^5 + 3*x^6 + x^7 - x^8 - x^9).
MATHEMATICA
a[n_] := Floor[n/2]^2 - Floor[n/3]^2
Table[a[n], {n, 0, 60}] (* A213029 *)
LinearRecurrence[{-1, 1, 3, 2, -2, -3, -1, 1, 1}, {0, 0, 1, 0, 3, 3, 5, 5, 12}, 60]
CoefficientList[Series[(x^2 + x^3 + 2 x^4 + 3 x^5 + 3 x^6) / (1 + x - x^2 - 3 x^3 - 2 x^4 + 2 x^5 + 3 x^6 + x^7 - x^8 - x^9), {x, 0, 80}], x] (* Vincenzo Librandi, Aug 02 2013 *)
PROG
(Magma) I:=[0, 0, 1, 0, 3, 3, 5, 5, 12]; [n le 9 select I[n] else -Self(n-1)+Self(n-2)+3*Self(n-3)+2*Self(n-4)-2*Self(n-5)-3*Self(n-6)-Self(n-7)+Self(n-8)+Self(n-9): n in [1..60]]; // Vincenzo Librandi, Aug 02 2013
CROSSREFS
Sequence in context: A245144 A279021 A339555 * A348843 A290208 A171710
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2012
EXTENSIONS
Formula corrected by Vincenzo Librandi, Aug 02 2013
STATUS
approved