A133252 Partial sums of A006000.

1, 5, 17, 45, 100, 196, 350, 582, 915, 1375, 1991, 2795, 3822, 5110, 6700, 8636, 10965, 13737, 17005, 20825, 25256, 30360, 36202, 42850, 50375, 58851, 68355, 78967, 90770, 103850, 118296, 134200, 151657, 170765, 191625, 214341, 239020, 265772

Offset: 0

Author

Jonathan Vos Post, Dec 19 2007

Keywords

• easy
• nonn

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A006000.

Programs

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{1,5,17,45,100},40] (* Harvey P. Dale, Sep 15 2022 *)

Formula

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

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

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.

G.f.: -(2*x^2 + 1) / (x-1)^5. - Colin Barker, Apr 28 2013

a(n) = (n+1)*(n+2)*(3*n^2+5*n+12)/24. - Alois P. Heinz, Apr 28 2013

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