A016815 (4n+1)^3.

1, 125, 729, 2197, 4913, 9261, 15625, 24389, 35937, 50653, 68921, 91125, 117649, 148877, 185193, 226981, 274625, 328509, 389017, 456533, 531441, 614125, 704969, 804357, 912673, 1030301, 1157625

Offset

0,2

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Formula

Sum_{n>=0} 1/a(n) = Pi^3/64 + 7 zeta(3)/16.

a(0)=1, a(1)=125, a(2)=729, a(3)=2197, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, Sep 01 2013

G.f.: ( 1+121*x+235*x^2+27*x^3 ) / (x-1)^4 . - R. J. Mathar, Dec 03 2015

Mathematica

(4*Range[0, 30]+1)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 125, 729, 2197}, 30] (* Harvey P. Dale, Sep 01 2013 *)

Crossrefs

Sequence in context: A251288 A060093 A253345 * A253352 A204611 A296037

Adjacent sequences: A016812 A016813 A016814 * A016816 A016817 A016818

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved