A152457 - OEIS

%I #17 Oct 21 2022 21:27:17

%S 0,3,17,56,140,295,553,952,1536,2355,3465,4928,6812,9191,12145,15760,

%T 20128,25347,31521,38760,47180,56903,68057,80776,95200,111475,129753,

%U 150192,172956,198215,226145,256928,290752,327811,368305,412440,460428

%N Partial sums of A027444.

%C 1^1+1^2+1^3=3; (2^1+2^2+2^3)+3=17; ...

%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(n + 1)(3n^2 + 7n + 8)/12. - _Giovanni Resta_, Jun 15 2013

%F a(0)=0, a(1)=3, a(2)=17, a(3)=56, a(4)=140, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - _Harvey P. Dale_, Dec 13 2013

%F G.f.: -x*(3+2*x+x^2) / (x-1)^5 . - _R. J. Mathar_, Jul 18 2016

%t Table[Sum[i + i^2 + i^3, {i, n}], {n, 0, 25}]

%t Accumulate[Table[n^3+n^2+n,{n,0,50}]] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,3,17,56,140},50] (* _Harvey P. Dale_, Dec 13 2013 *)

%o (PARI) a(n)=n*(n+1)*(3*n^2+7*n+8)/12 \\ _Charles R Greathouse IV_, Oct 21 2022

%K nonn,easy

%O 0,2

%A _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008

%E Definition corrected by _Jeremy Gardiner_, Jun 15 2013