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A098821
a(n) = (n-2) * 2^(n-1) + 5.
0
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
0,1
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)
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)
EXAMPLE
a(5) = 3*2^4 + 5 = 53.
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 *)
PROG
(PARI) a(n)=(n-2)<<(n-1)+5 \\ Charles R Greathouse IV, Jul 23 2015
CROSSREFS
Sequence in context: A160705 A107851 A302337 * A363322 A374754 A142154
KEYWORD
nonn,easy
AUTHOR
Parthasarathy Nambi, Oct 08 2004
EXTENSIONS
More terms from Stefan Steinerberger, Mar 06 2006
STATUS
approved