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A213038
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a(n) = n^2 - 3*floor(n/2)^2.
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1
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0, 1, 1, 6, 4, 13, 9, 22, 16, 33, 25, 46, 36, 61, 49, 78, 64, 97, 81, 118, 100, 141, 121, 166, 144, 193, 169, 222, 196, 253, 225, 286, 256, 321, 289, 358, 324, 397, 361, 438, 400, 481, 441, 526, 484, 573, 529, 622, 576, 673, 625, 726, 676, 781, 729, 838
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OFFSET
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0,4
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
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FORMULA
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a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: x*(1+3*x^2-2*x^3) / ((1-x)^3*(1+x)^2). [Corrected by Colin Barker, Jan 26 2016]
a(n) = ( 2*n*(n+3) - 3*(2*n-1)*(-1)^n - 3 )/8. [Bruno Berselli, Jan 26 2016]
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MATHEMATICA
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a[n_] := n^2 - 3 Floor[n/2]^2
Table[a[n], {n, 0, 90}] (* A213038 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 1, 6, 4}, 60] (* Harvey P. Dale, Sep 22 2019 *)
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PROG
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(PARI) concat(0, Vec(x*(1+3*x^2-2*x^3)/((1-x)^3*(1+x)^2) + O(x^100))) \\ Colin Barker, Jan 26 2016
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CROSSREFS
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Sequence in context: A006582 A263586 A180497 * A337512 A131828 A096038
Adjacent sequences: A213035 A213036 A213037 * A213039 A213040 A213041
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 06 2012
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STATUS
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approved
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