A186684 Total number of positive integers below 10^n requiring 19 positive biquadrates in their representation as sum of biquadrates.

0, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

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) + A186680(n) + A186682(n) + a(n) = A002283(n).

References

• J.-M. Deshouillers, K. Kawada, and T. D. Wooley, On sums of sixteen biquadrates, Mem. Soc. Math. Fr. 100 (2005), p. 120.

Links

• J.-M. Deshouillers, F. Hennecart and B. Landreau, Waring's Problem for sixteen biquadrates - numerical results, Journal de Théorie des Nombres de Bordeaux 12 (2000), pp. 411-422.
• L. E. Dickson, Recent progress on Waring's theorem and its generalizations, Bull. Amer. Math. Soc. 39:10 (1933), pp. 701-727.
• Eric Weisstein's World of Mathematics, Waring's Problem.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A010727, A046050.

Programs

Mathematica

PadRight[{0, 1}, 100, 7] (* Paolo Xausa, Jul 30 2024 *)

Formula

a(n) = 7 for n >= 3. - Nathaniel Johnston, May 09 2011

From Elmo R. Oliveira, Aug 05 2024: (Start)

G.f.: x^2*(1 + 6*x)/(1 - x).

E.g.f.: 7*(exp(x) - 1 - x) - 3*x^2. (End)

Extensions

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

Terms after a(6) from Nathaniel Johnston, May 09 2011