A133252 - OEIS

%I #14 Apr 21 2024 22:04:00

%S 1,5,17,45,100,196,350,582,915,1375,1991,2795,3822,5110,6700,8636,

%T 10965,13737,17005,20825,25256,30360,36202,42850,50375,58851,68355,

%U 78967,90770,103850,118296,134200,151657,170765,191625,214341,239020,265772

%N Partial sums of A006000.

%C Prime for a(1) = 5, a(2) = 17, then never again?

%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) = Sum_{i=0..n} A006000(i).

%F a(n) = Sum_{i=0..n} (i+1)*(i^2+i+2)/2.

%F a(n) = ((n^4+2*n^3+n^2)/4+(2*n^3+3*n^2+n)/3+(3*n^2+3*n)/2+2*n)/2+1.

%F G.f.: -(2*x^2 + 1) / (x-1)^5. - _Colin Barker_, Apr 28 2013

%F a(n) = (n+1)*(n+2)*(3*n^2+5*n+12)/24. - _Alois P. Heinz_, Apr 28 2013

%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Apr 21 2024

%t LinearRecurrence[{5,-10,10,-5,1},{1,5,17,45,100},40] (* _Harvey P. Dale_, Sep 15 2022 *)

%Y Cf. A006000.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Dec 19 2007