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A204556 Left edge of the triangle A045975.

%I A204556 #25 Sep 08 2022 08:46:01
%S A204556 1,2,9,24,45,90,133,224,297,450,561,792,949,1274,1485,1920,2193,2754,
%T A204556 3097,3800,4221,5082,5589,6624,7225,8450,9153,10584,11397,13050,13981,
%U A204556 15872,16929,19074,20265,22680,24013,26714,28197,31200,32841,36162,37969,41624
%N A204556 Left edge of the triangle A045975.
%H A204556 G. C. Greubel, <a href="/A204556/b204556.txt">Table of n, a(n) for n = 1..5000</a>
%H A204556 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A204556 a(n) = A045975(n,1);
%F A204556 a(n) = A031940(n-1) * n for n > 1;
%F A204556 a(n) = A204557(n) - A045895(n).
%F A204556 G.f.: x*(1+x+4*x^2+12*x^3+3*x^4+3*x^5) / ((1+x)^3*(x-1)^4). - _R. J. Mathar_, Aug 13 2012
%F A204556 From _Colin Barker_, Jan 28 2016: (Start)
%F A204556 a(n) = n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4.
%F A204556 a(n) = (n^3-n^2)/2 for n even.
%F A204556 a(n) = (n^3-2*n^2+3*n)/2 for n odd.
%F A204556 (End)
%t A204556 Table[n*(2*n^2 - 3*n + (-1)^n*(n - 3) + 3)/4, {n, 1, 50}] (* _G. C. Greubel_, Jun 15 2018 *)
%o A204556 (Haskell)
%o A204556 a204556 = head . a045975_row
%o A204556 (PARI) Vec(x*(1+x+4*x^2+12*x^3+3*x^4+3*x^5)/((1+x)^3*(x-1)^4) + O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2015
%o A204556 (PARI) for(n=1, 50, print1(n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4, ", ")) \\ _G. C. Greubel_, Jun 15 2018
%o A204556 (Magma) [n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4: n in [1..50]]; // _G. C. Greubel_, Jun 15 2018
%K A204556 nonn,easy
%O A204556 1,2
%A A204556 _Reinhard Zumkeller_, Jan 18 2012