

A039596


Numbers that are simultaneously triangular and square pyramidal.


8




OFFSET

1,2


COMMENTS

Equivalent to 1^2 + 2^2 + 3^2 + ... + r^2 = 1 + 2 + 3 + ... + s = n for some r and s.


REFERENCES

Joe Roberts, Lure of the Integers, page 245 (entry for 645).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, p. 108.


LINKS

Table of n, a(n) for n=1..4.
R. Finkelstein, H. London, On triangular numbers which are sums of consecutive squares, J. Number Theory 4 (1972), 455462.
M. Gardner, Letter to N. J. A. Sloane, circa Aug 11 1980, concerning A001110, A027568, A039596, etc.
H. E. Thomas Jr., Problem 5634, Amer. Math. Monthly, 75 (1968), p. 1018.


EXAMPLE

1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 2 + 3 + ... + 10 = 55, so 55 is in the sequence.


CROSSREFS

Cf. A000217, A000330, A053611, A053612.
Sequence in context: A063873 A063131 A128880 * A013543 A115377 A146145
Adjacent sequences: A039593 A039594 A039595 * A039597 A039598 A039599


KEYWORD

fini,nonn,full


AUTHOR

Felice Russo


EXTENSIONS

Additional comments from Jud McCranie, Mar 19 2000


STATUS

approved



