login
Row sums of unsigned A128090.
1

%I #17 Sep 20 2024 03:20:33

%S 1,8,45,160,425,936,1813,3200,5265,8200,12221,17568,24505,33320,44325,

%T 57856,74273,93960,117325,144800,176841,213928,256565,305280,360625,

%U 423176,493533,572320,660185,757800,865861,985088,1116225,1260040,1417325

%N Row sums of unsigned A128090.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).

%F a(n) = (n-1)*A045991(n) + n^2.

%F a(n) = n^2*(n^2 - 2*n + 2) = A000290(n)*A002522(n-1). - _Philippe Deléham_, Mar 16 2014

%F G.f.: x*(1 + 3*x + 15*x^2 + 5*x^3)/(1-x)^5. - _Philippe Deléham_, Mar 16 2014

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), a(1) = 1, a(2) = 8, a(3) = 45, a(4) = 160, a(5) = 425. - _Philippe Deléham_, Mar 16 2014

%e a(4) = 160 = sum of row 4 terms of A128090: (48 + 48 + 48 + 16) = 3*A045991(4) + 4^2; where A045991 = (0, 0, 4, 18, 48, 100, ...).

%o (PARI) a(n)=n^2*(n^2 - 2*n + 2) \\ _Charles R Greathouse IV_, Oct 21 2022

%Y Cf. A000290, A002522, A128077, A128090, A045991.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Feb 14 2007

%E a(10)-a(35) from _Philippe Deléham_, Mar 16 2014