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

0,2

Comments

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

Links

Table of n, a(n) for n=0..37.

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

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

Mathematica

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

Crossrefs

Cf. A006000.

Sequence in context: A190969 A099451 A174794 * A299335 A247618 A269962

Adjacent sequences: A133249 A133250 A133251 * A133253 A133254 A133255

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 19 2007

Status

approved