1,2

Numbers n such that n-th triangular number - n is a square.

Gives solutions to A007913(2x)=A007913(x-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 07 2002

Number of closed walks of length 2n on the grid graph P_2 X P_3. - Mitch Harris, Mar 06 2004

a(2k) = A001541(k)^2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 24 2006

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.

P. Lafer, Discovering the square-triangular numbers, Fib. Quart., 9 (1971), 93-105.

a(n) = 6a(n-1)-a(n-2)-2; n >= 2, a(0) = 1, a(1) = 2. G.f.(x) = (1-5x+2x^2)/((1-x)(1-6x+x^2)).

a(n)-1+(2*a(n)*(a(n)-1))^.5 = A001652(n); e.g. 50-1+(2*50*49)^.5 = 119 - Charlie Marion (charliem(AT)bestweb.net), Jul 21 2003

a(n) = IF(mod(n; 2)=0; (((1-SQRT(2))^n+(1+SQRT(2))^n)/2)^2; 2*((((1-SQRT(2))^(n+1)+(1+SQRT(2))^(n+1))-(((1-SQRT(2))^n+(1+SQRT(2))^n)))/4)^2). The even-indexed terms are a(n) = [A001333(n)]^2; the odd-indexed terms are a(n) = 2*[ [A001333(n+1) - A001333(n)]/4 ]^2 = 2*[ [A001333(n+1) - A001333(n)]/4 ]^2 = 2*[A001653(n)]^2. - Antonio Alberto Olivares (tonioolivares(AT)todito.com), Jan 31 2004

A053141(n+1) + a(n+1) = A001541(n+1) + A001109(n+1). - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Sep 16 2004

a(n) = (1/2) + (1/4)(3+2*SQRT(2))^n + (1/4)(3-2*SQRT(2))^n. - Antonio Alberto Olivares (tonioolivares(AT)todito.com), Feb 21 2006

a(n)=A001653(n)-A001652(n); e.g. 50=169-119 - Charlie Marion (charliemath(AT)optonline.net) Apr 10 2006

A001109(n) = sqrt{[(a(n))^2 - (a(n))]/2}.

a(n) = A001108(n)+1. Cf. A001109.

Cf. A007913.

Cf. A001541.

Sequence in context: A109323 A014372 A138416 this_sequence A047069 A020087 A079836

Adjacent sequences: A055994 A055995 A055996 this_sequence A055998 A055999 A056000

easy,nice,nonn

Barry E. Williams, Jun 14 2000