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%I #28 Jul 30 2023 17:45:14
%S 0,4,16,44,96,180,304,476,704,996,1360,1804,2336,2964,3696,4540,5504,
%T 6596,7824,9196,10720,12404,14256,16284,18496,20900,23504,26316,29344,
%U 32596,36080,39804,43776,48004,52496,57260,62304,67636,73264,79196,85440,92004
%N a(n) = 4*n*(n^2 + 2)/3.
%C Occurs as 4th column in the table A142978 of figurate numbers for n-dimensional cross polytope.
%H Vincenzo Librandi, <a href="/A217873/b217873.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 4*A006527(n).
%F From _Peter Luschny_, Oct 14 2012: (Start)
%F a(n) = A008412(n)/2
%F a(n) = A174794(n + 1) - 1
%F First differences are in A112087.
%F Second differences are in A008590 and A022144.
%F Binomial transformation of (a(n), n > 0) is A082138. (End)
%F G.f. 4*x*(1 + x^2) / (x - 1)^4 . - _R. J. Mathar_, Oct 15 2012
%F 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
%t Table[4n(n^2 + 2)/3, {n, 0, 39}] (* _Alonso del Arte_, Oct 22 2012 *)
%t LinearRecurrence[{4,-6,4,-1},{0,4,16,44},50] (* _Harvey P. Dale_, Mar 16 2015 *)
%o (PARI) a(n)=(n^2+2)*n/3*4
%o (Maxima) makelist(4*n*(n^2+2)/3, n, 0, 41); /* _Martin Ettl_, Oct 15 2012] */
%o (Magma) [4*n*(n^2+2)/3: n in [0..45]]; // _Vincenzo Librandi_, Nov 08 2012
%K nonn,easy
%O 0,2
%A _M. F. Hasler_, Oct 13 2012
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