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0, 4, 16, 44, 96, 180, 304, 476, 704, 996, 1360, 1804, 2336, 2964, 3696, 4540, 5504, 6596, 7824, 9196, 10720, 12404, 14256, 16284, 18496, 20900, 23504, 26316, 29344, 32596, 36080, 39804, 43776, 48004, 52496, 57260, 62304, 67636, 73264, 79196, 85440, 92004
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OFFSET
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0,2
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COMMENTS
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Occurs as 4th column in the table A142978 of figurate numbers for n-dimensional cross polytope.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = 4*A006527(n)
From Peter Luschny, Oct 14 2012: (Start)
a(n) = A008412(n)/2
a(n) = A174794(n + 1) - 1
First differences are in A112087.
Second differences are in A008590 and A022144.
Binomial transformation of (a(n), n > 0) is A082138. (End)
G.f. 4*x*(1 + x^2) / (x - 1)^4 . - R. J. Mathar, Oct 15 2012
a(0)=0, a(1)=4, a(2)=16, a(3)=44, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Mar 16 2015
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MATHEMATICA
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Table[4n(n^2 + 2)/3, {n, 0, 39}] (* Alonso del Arte, Oct 22 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 16, 44}, 50] (* Harvey P. Dale, Mar 16 2015 *)
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PROG
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(PARI) a(n)=(n^2+2)*n/3*4
(Maxima) makelist(4*n*(n^2+2)/3, n, 0, 41); /* Martin Ettl, Oct 15 2012] */
(Magma) [4*n*(n^2+2)/3: n in [0..45]]; // Vincenzo Librandi, Nov 08 2012
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CROSSREFS
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Sequence in context: A161142 A259013 A212960 * A289086 A018210 A054498
Adjacent sequences: A217870 A217871 A217872 * A217874 A217875 A217876
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KEYWORD
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nonn,easy
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AUTHOR
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M. F. Hasler, Oct 13 2012
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STATUS
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approved
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