A204557 - OEIS

%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