OFFSET
1,2
COMMENTS
a(n) = (Q-1)*(2^n) + (2^n-1)*(1^n) is a sum of Q + 2^n - 2 terms, Q = trunc(3^n / 2^n).
REFERENCES
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 393.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..200
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, exercise 7.1.1. p. 277.
Eric Weisstein's World of Mathematics, Waring's Problem.
FORMULA
a(n) = 2^n*floor((3/2)^n) - 1 = 2^n*A002379(n) - 1.
EXAMPLE
a(3) = 23 = 16 + 7 = 2*(2^3) + 7*(1^3) is a sum of 9 cubes;
a(4) = 79 = 64 + 15 = 4*(2^4) + 15*(1^4) is a sum of 19 biquadrates.
MAPLE
MATHEMATICA
a[n_]:=-1+2^n*Floor[(3/2)^n]
a[Range[1, 20]] (* Julien Kluge, Jul 21 2016 *)
PROG
(Python)
def a(n): return (3**n//2**n-1)*2**n + (2**n-1)
print([a(n) for n in range(1, 27)]) # Michael S. Branicky, Dec 17 2021
(Python)
def A018886(n): return (3**n&-(1<<n))-1 # Chai Wah Wu, Jun 25 2024
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved