A186680 Total number of positive integers below 10^n requiring 17 positive biquadrates in their representation as sum of biquadrates.

0, 3, 33, 63, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65

Offset: 1

Author

Martin Renner, Feb 25 2011

Keywords

• nonn
• easy

Comments

A114322(n) + A186649(n) + A186651(n) + A186653(n) + A186655(n) + A186657(n) + A186659(n) + A186661(n) + A186663(n) + A186665(n) + A186667(n) + A186669(n) + A186671(n) + A186673(n) + A186675(n) + A186677(n) + a(n) + A186682(n) + A186684(n) = A002283(n)

a(n) = 65 for n >= 5. - Nathaniel Johnston, May 09 2011

Continued fraction expansion of (826055+sqrt(4229))/2503382. - Bruno Berselli, May 10 2011

Links

• Eric Weisstein's World of Mathematics, Waring's Problem.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A046048, A099591.

Programs

Mathematica

PadRight[{0, 3, 33, 63}, 100, 65] (* Paolo Xausa, Jul 31 2024 *)

Formula

G.f.: x^2*(3+30*x+30*x^2+2*x^3)/(1-x). - Bruno Berselli, May 10 2011

Extensions

a(5)-a(6) from Lars Blomberg, May 08 2011

a(7) from Charles R Greathouse IV, May 08 2011

Terms after a(7) from Nathaniel Johnston, May 09 2011