0,2

Or triangular numbers such that distance to the nearest square is 1. [From Ctibor O. ZIZKA (c.zizka(AT)email.cz), Oct 07 2009]

Also numbers n such that (ceiling(sqrt(n*(n+1)/2)))^2 - n*(n+1)/2 = 1. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 10 2009]

A. J. Gottlieb, How four dogs meet in a field, etc., Technology Review, Problem J/A2, Jul/August 1973 pp. 73-74; solution Jan 1974 (see link).

J. O. Shallit, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. J. Gottlieb, How four dogs meet in a field, etc. (scanned copy)

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n)=6a(n-2)-a(n-4)+2 with a(0)=0, a(1)=2, a(2)=5, a(3)=15. - Zak Seidov, Apr 15 2008

A006451:=z*(-2-3*z+2*z**2+z**3)/(z-1)/(z**2+2*z-1)/(z**2-2*z-1); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]

for(n=1, 10000, t=n*(n+1)/2+1; if(issquare(t), print1(n, ", "))) - Joerg Arndt, Oct 10 2009

Cf. A000124, A006452, A006454.

Sequence in context: A078528 A077686 A034499 this_sequence A000962 A118387 A034522

Adjacent sequences: A006448 A006449 A006450 this_sequence A006452 A006453 A006454

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com) and Jeffrey Shallit

More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001

Edited by N. J. A. Sloane, Oct 24 2009, following discussions by several correspondents in the Sequence Fans Mailing List, Oct 10 2009