%I A055997
%S A055997 1,2,9,50,289,1682,9801,57122,332929,1940450,11309769,65918162,
%T A055997 384199201,2239277042,13051463049,76069501250,443365544449,
%U A055997 2584123765442,15061377048201,87784138523762,511643454094369
%N A055997 Numbers n such that n(n-1)/2 is a square.
%C A055997 Numbers n such that n-th triangular number - n is a square.
%C A055997 Gives solutions to A007913(2x)=A007913(x-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 07 2002
%C A055997 Number of closed walks of length 2n on the grid graph P_2 X P_3. - Mitch 
               Harris, Mar 06 2004
%C A055997 a(2k) = A001541(k)^2. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Nov 24 2006
%D A055997 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               p. 193.
%D A055997 P. Lafer, Discovering the square-triangular numbers, Fib. Quart., 9 (1971), 
               93-105.
%F A055997 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)).
%F A055997 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
%F A055997 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-SQ\
               RT(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
%F A055997 A053141(n+1) + a(n+1) = A001541(n+1) + A001109(n+1). - Creighton Dement 
               (creighton.k.dement(AT)uni-oldenburg.de), Sep 16 2004
%F A055997 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
%F A055997 a(n)=A001653(n)-A001652(n); e.g. 50=169-119 - Charlie Marion (charliemath(AT)optonline.net) 
               Apr 10 2006
%Y A055997 A001109(n) = sqrt{[(a(n))^2 - (a(n))]/2}.
%Y A055997 a(n) = A001108(n)+1. Cf. A001109.
%Y A055997 Cf. A007913.
%Y A055997 Cf. A001541.
%Y A055997 Sequence in context: A109323 A014372 A138416 this_sequence A047069 A020087 
               A079836
%Y A055997 Adjacent sequences: A055994 A055995 A055996 this_sequence A055998 A055999 
               A056000
%K A055997 easy,nice,nonn
%O A055997 1,2
%A A055997 Barry E. Williams, Jun 14 2000