|
Search: id:A053604
|
|
|
| A053604 |
|
Number of ways to write n as an ordered sum of 3 nonzero triangular numbers. |
|
+0
5
|
|
| 0, 0, 0, 1, 0, 3, 0, 3, 3, 1, 6, 0, 6, 3, 6, 3, 3, 9, 1, 12, 0, 6, 9, 6, 6, 6, 9, 6, 12, 0, 10, 9, 12, 6, 9, 9, 3, 18, 3, 12, 12, 9, 9, 9, 12, 10, 12, 9, 9, 18, 6, 6, 27, 6, 12, 6, 9, 18, 15, 15, 6, 21, 9, 13, 12, 9, 18, 21, 9, 6, 21, 15, 15, 15, 12, 15, 18, 15, 9
(list; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
Fermat asserted that every number is the sum of three triangular numbers. This was proved by Gauss, who recorded in his Tagebuch entry for Jul 10 1796 that: EYPHEKA! num = DELTA + DELTA + DELTA.
|
|
REFERENCES
|
Mel Nathanson, Additive Number Theory: The Classical Bases, Graduate Texts in Mathematics, Volume 165, Springer-Verlag, 1996. See Chapter 1.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..5050
|
|
CROSSREFS
|
Cf. A000217, A007294, A051611, A051533, A053604, A053603, A008443, A002636.
Sequence in context: A127801 A096597 A097994 this_sequence A066958 A066851 A167223
Adjacent sequences: A053601 A053602 A053603 this_sequence A053605 A053606 A053607
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Jan 20 2000
|
|
|
Search completed in 0.002 seconds
|
