A098821 a(n) = (n-2) * 2^(n-1) + 5.

4, 4, 5, 9, 21, 53, 133, 325, 773, 1797, 4101, 9221, 20485, 45061, 98309, 212997, 458757, 983045, 2097157, 4456453, 9437189, 19922949, 41943045, 88080389, 184549381, 385875973, 805306373, 1677721605, 3489660933, 7247757317

Offset: 0

Author

Parthasarathy Nambi, Oct 08 2004

Keywords

• nonn
• easy

Examples

			a(5) = 3*2^4 + 5 = 53.
		

References

• G. H. Hardy and J. E. Littlewood, "Some problems of partitio numerorum (VI): Further researches in Waring's Problem", Math. Z. vol. 23, 1-37, (1925)
• T. D. Wooley, "Large improvements in Waring's Problem", Ann. Math. vol. 135, 131-164 (1992)

Links

• Eric Weisstein, Waring's problem
• Index entries for linear recurrences with constant coefficients, signature (5, -8, 4).

Crossrefs

Cf. A018889, A002804.

Programs

Mathematica

Table[(n - 2)*2^(n - 1) + 5, {n, 0, 30}] (* Stefan Steinerberger, Mar 06 2006 *)
LinearRecurrence[{5,-8,4},{4,4,5},40] (* Harvey P. Dale, Feb 22 2013 *)

PARI

a(n)=(n-2)<<(n-1)+5 \\ Charles R Greathouse IV, Jul 23 2015

Formula

From Colin Barker, Jan 28 2012: (Start)

G.f.: (4-16*x+17*x^2)/(1-5*x+8*x^2-4*x^3).

a(n)=5*a(n-1)-8*a(n-2)+4*a(n-3). (End)

Extensions

More terms from Stefan Steinerberger, Mar 06 2006