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A064835
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If n mod 2 = 0 then a(n) = n^4/4 - 2*n^2 + 3*n; otherwise, a(n) = n^4/4 - 2*n^2 + 3*n - 5/4.
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2
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0, 0, 2, 10, 44, 120, 270, 522, 920, 1504, 2330, 3450, 4932, 6840, 9254, 12250, 15920, 20352, 25650, 31914, 39260, 47800, 57662, 68970, 81864, 96480, 112970, 131482, 152180, 175224, 200790, 229050, 260192, 294400, 331874, 372810, 417420, 465912, 518510, 575434
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: 2*x^2*(1+x+7*x^2-3*x^3)/((1-x)^5*(1+x)). [Colin Barker, Apr 20 2012]
a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6). - Vincenzo Librandi, Jun 19 2018
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MATHEMATICA
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Table[If[EvenQ[n], n^4/4-2n^2+3n, n^4/4-2n^2+3n-5/4], {n, 0, 40}] (* Harvey P. Dale, Dec 02 2014 *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 0, 2, 10, 44, 120}, 40] (* Vincenzo Librandi, Jun 19 2018 *)
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PROG
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(PARI) { for (n=0, 1000, a=n^4/4 - 2*n^2 + 3*n; if (n%2, a-=5/4); write("b064835.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 28 2009
(Magma) I:=[0, 0, 2, 10, 44, 120]; [n le 6 select I[n] else 4*Self(n-1) - 5*Self(n-2) + 5*Self(n-4) - 4*Self(n-5) + Self(n-6): n in [1..40]]; // Vincenzo Librandi, Jun 19 2018
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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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