A098821 - OEIS

%I #19 Aug 26 2015 21:38:34

%S 4,4,5,9,21,53,133,325,773,1797,4101,9221,20485,45061,98309,212997,

%T 458757,983045,2097157,4456453,9437189,19922949,41943045,88080389,

%U 184549381,385875973,805306373,1677721605,3489660933,7247757317

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

%D 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)

%D T. D. Wooley, "Large improvements in Waring's Problem", Ann. Math. vol. 135, 131-164 (1992)

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Waring's problem</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, -8, 4).

%F From _Colin Barker_, Jan 28 2012: (Start)

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

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

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

%t Table[(n - 2)*2^(n - 1) + 5, {n, 0, 30}] (* _Stefan Steinerberger_, Mar 06 2006 *)

%t LinearRecurrence[{5,-8,4},{4,4,5},40] (* _Harvey P. Dale_, Feb 22 2013 *)

%o (PARI) a(n)=(n-2)<<(n-1)+5 \\ _Charles R Greathouse IV_, Jul 23 2015

%Y Cf. A018889, A002804.

%K nonn,easy

%O 0,1

%A _Parthasarathy Nambi_, Oct 08 2004

%E More terms from _Stefan Steinerberger_, Mar 06 2006