%I A082840
%S A082840 1,1,8,34,131,493,1844,6886,25703,95929,358016,1336138,4986539,18610021,
               69453548,
%T A082840 259204174,967363151,3610248433,13473630584,50284273906,187663465043,700369586269,
%U A082840 2613814880036,9754889933878,36405744855479,135868089488041
%V A082840 -1,1,8,34,131,493,1844,6886,25703,95929,358016,1336138,4986539,18610021,
               69453548,
%W A082840 259204174,967363151,3610248433,13473630584,50284273906,187663465043,700369586269,
%X A082840 2613814880036,9754889933878,36405744855479,135868089488041
%N A082840 a(n)=4a(n-1)-a(n-2)+3.
%C A082840 Apart from the initial -1, these are the numbers k such that the triangular 
               number k(k+1)/2 is the sum of three consecutive triangular numbers 
               - see A129803. - Brian Nowell <brianjnow@iinet.net.au>, Nov 03 2009
%F A082840 a(n) = A001571(n) - 1. - njas, Nov 03 2009
%F A082840 G.f.: (-1+6x-2x^2)/((1-x)(1-4x+x^2)). With a=2+sqrt(3), b=2-sqrt(3): 
               a(n)=-3/2+(1/12)(a-2b+5)a^n+(1/12)(b-2a+5)b^n. a(n)=-3/2 +(3/4)A003500(n)- 
               (1/4)A003500(n-1). a(n)=(1/2)(A001834(n)-3).
%Y A082840 Sequence in context: A033455 A053298 A124843 this_sequence A101644 A126395 
               A158991
%Y A082840 Adjacent sequences: A082837 A082838 A082839 this_sequence A082841 A082842 
               A082843
%K A082840 easy,sign,new
%O A082840 0,3
%A A082840 Mario Catalani (mario.catalani(AT)unito.it), Apr 14 2003