A083559 Nearest integer to 1/(Sum_{k>=n} 1/k^4).

1, 12, 50, 134, 280, 507, 834, 1277, 1855, 2586, 3489, 4580, 5878, 7401, 9168, 11195, 13501, 16104, 19023, 22274, 25876, 29847, 34206, 38969, 44155, 49782, 55869, 62432, 69490, 77061, 85164, 93815, 103033, 112836, 123243, 134270, 145936

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-3,3,-1).

Formula

a(n) = floor(3*n^3-9/2*n^2+15/4*n-3/4) for n > 3.

G.f.: -x*(x^9-3*x^8+3*x^7-2*x^6-10*x^5-15*x^4-19*x^3-17*x^2-9*x-1) / ((x-1)^4*(x+1)*(x^2+1)). - Colin Barker, Dec 01 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7). - Wesley Ivan Hurt, Apr 20 2021

Mathematica

LinearRecurrence[{3, -3, 1, 1, -3, 3, -1}, {1, 12, 50, 134, 280, 507, 834, 1277, 1855, 2586}, 40] (* Harvey P. Dale, Sep 18 2018 *)

Prog

(PARI) a(n)=round(1/(zeta(4)-sum(k=1, n-1, 1/k^4)))

Crossrefs

Cf. A001844.

Sequence in context: A009938 A063491 A248230 * A051797 A342482 A333276

Adjacent sequences: A083556 A083557 A083558 * A083560 A083561 A083562

Keyword

nonn,easy

Author

Benoit Cloitre, Jun 12 2003

Status

approved