1,2

These are the only possibilities for a sum of the first n squares to equal a triangular number.

E. T. Avanesov, The Diophantine equation 3y(y+1) = x(x+1)(2x+1), Volz. Mat. Sb. Vyp., 8 (1971), 3-6.

R. Finkelstein and H. London, On triangular numbers which are sums of consecutive squares, J. Number Theory, 4 (1972), 455-462.

Joe Roberts, Lure of the Integers, page 245 (entry for 645).

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

istriangular:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then RETURN(true) else RETURN(false); fi; end;

M:=1000; for n from 1 to M do if istriangular(n*(n+1)*(2*n+1)/6) then lprint(n, n*(n+1)*(2*n+1)/6); fi; od: (Maple program from N. J. A. Sloane (njas(AT)research.att.com))

Cf. A039596 (values of s), A053612.

Sequence in context: A111504 A041057 A041058 this_sequence A041139 A065354 A078984

Adjacent sequences: A053608 A053609 A053610 this_sequence A053612 A053613 A053614

fini,full,nonn,bref

Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000

Edited by N. J. A. Sloane (njas(AT)research.att.com), May 25 2008