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A177058
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n^3 - 3n^2 + 3.
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2
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3, 1, -1, 3, 19, 53, 111, 199, 323, 489, 703, 971, 1299, 1693, 2159, 2703, 3331, 4049, 4863, 5779, 6803, 7941, 9199, 10583, 12099, 13753, 15551, 17499, 19603, 21869, 24303, 26911, 29699, 32673, 35839, 39203, 42771, 46549, 50543, 54759, 59203
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OFFSET
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0,1
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COMMENTS
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For n>2, fourth diagonal of A162611.
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LINKS
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B. Berselli, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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Contribution from Bruno Berselli, Jun 04 2010: (Start)
G.f.: (3-11*x+13*x^2+x^3)/(1-x)^4.
a(n)-4*a(n-1)+6*a(n-2)-4*a(n-3)+a(n-4) = 0, with n>3.
a(n)+a(n-1) = 2*A081438(n-3), with n>2. (End)
G.f.: 3+x+x^2*G(0) where G(k)= 1 - x*(k+1)*(k+1)*(k+4)/(1 - 1/(1 - (k+1)*(k+1)*(k+4)/G(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 16 2012
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MATHEMATICA
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Table[n^3-3n^2+3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {3, 1, -1, 3}, 50] (* Harvey P. Dale, May 15 2020 *)
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PROG
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(PARI) a(n)=n^3-3*n^2+3 \\ Charles R Greathouse IV, Jan 11 2012
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CROSSREFS
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Cf. A162611, A081438.
Sequence in context: A245537 A277198 A242735 * A176921 A000503 A254864
Adjacent sequences: A177055 A177056 A177057 * A177059 A177060 A177061
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KEYWORD
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sign,easy
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AUTHOR
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Vincenzo Librandi, May 27 2010
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STATUS
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approved
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