A186684 - OEIS

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

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OFFSET

1,3

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

Table of n, a(n) for n=1..87.

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).

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)

MATHEMATICA

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

CROSSREFS

Cf. A010727, A046050.