

A214900


Number of ordered ways to represent n as the sum of three squares and one fourth power.


0



1, 4, 6, 4, 4, 9, 9, 3, 3, 9, 12, 9, 4, 7, 12, 6, 4, 15, 18, 10, 12, 18, 12, 3, 6, 18, 27, 19, 5, 18, 24, 6, 6, 18, 21, 18, 18, 18, 18, 9, 9, 30, 33, 13, 6, 27, 24, 6, 4, 16, 33, 27, 18, 24, 33, 12, 12, 27, 18, 18, 12, 24, 30, 12, 4, 30, 45, 21, 18, 33, 30, 6, 12, 21, 33, 34, 10, 27, 30, 6, 9, 40, 39, 24, 25, 33, 39, 18, 9
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Different orderings of summands are counted, e.g., 1 = 1^2 + 0^2 + 0^4 + 0^4 = 0^2 + 1^2 + 0^4 + 0^4 = 0^2 + 0^2 + 1^4 + 0^4 = 0^2 + 0^2 + 0^4 + 1^4, so a(1)=4.
Conjecture: a(n) != 0, that is, all numbers are sums of three squares and one fourth power.


LINKS

Table of n, a(n) for n=0..88.


FORMULA

G.f.: (Sum_{j>=0} x^(j^2))^3 * (Sum_{j>=0} x^(j^4)) (see PARI code).


PROG

(PARI)
N=10^3; x='x+O('x^N);
S(e)=sum(j=0, ceil(N^(1/e)), x^(j^e));
v=Vec( S(4)^1 * S(2)^3 )


CROSSREFS

Cf. A000925 (two squares), A002102 (three squares).
Sequence in context: A161965 A256419 A256424 * A078385 A137444 A137429
Adjacent sequences: A214897 A214898 A214899 * A214901 A214902 A214903


KEYWORD

nonn


AUTHOR

Joerg Arndt, Jul 29 2012


STATUS

approved



