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A133252
Partial sums of A006000.
1
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?
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 19 2007
STATUS
approved