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%I #23 Sep 08 2022 08:46:01
%S 1,4,21,36,85,120,217,280,441,540,781,924,1261,1456,1905,2160,2737,
%T 3060,3781,4180,5061,5544,6601,7176,8425,9100,10557,11340,13021,13920,
%U 15841,16864,19041,20196,22645,23940,26677,28120,31161,32760,36121,37884,41581
%N Right edge of the triangle A045975.
%H Colin Barker, <a href="/A204557/b204557.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F a(n) = A045975(n,n);
%F a(n) = A079326(n+1) * n;
%F a(n) = A204556(n) + A045895(n).
%F G.f.: -x*(-1-3*x-14*x^2-6*x^3-x^4+x^5) / ((1+x)^3*(x-1)^4). - _R. J. Mathar_, Aug 13 2012
%F From _Colin Barker_, Jan 28 2016: (Start)
%F a(n) = n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4.
%F a(n) = (n^3+n^2-2*n)/2 for n even.
%F a(n) = (n^3+2*n^2-n)/2 for n odd.
%F (End)
%t Table[n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4, {n, 1, 50}] (* _G. C. Greubel_, Jun 15 2018 *)
%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,4,21,36,85,120,217},50] (* _Harvey P. Dale_, Feb 20 2021 *)
%o (Haskell)
%o a204557 = last . a045975_row
%o (PARI) Vec(-x*(-1-3*x-14*x^2-6*x^3-x^4+x^5)/((1+x)^3*(x-1)^4) + O(x^100)) \\ _Colin Barker_, Jan 28 2016
%o (Magma) [n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4: n in [1..50]]; // _G. C. Greubel_, Jun 15 2018
%K nonn,easy
%O 1,2
%A _Reinhard Zumkeller_, Jan 18 2012
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