# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a152121 Showing 1-1 of 1 %I A152121 #3 Nov 11 2010 07:34:06 %S A152121 4,12,136,18464,340918784,116225617283907584, %T A152121 13508394113025357323362163662782464, %U A152121 182476711512818130204254420972394401125552102555370860811711166808064 %N A152121 a(0) = 4; for n>0, a(n) = a(n-1)^2 - 2^(1+2^(n-1)) %C A152121 A subset of A056236, where a(n) = (2+sqrt(2))^n+(2-sqrt(2))^n, when the exponent n is a nonnegative integer power of 2. I.E.: a(0) = (2+sqrt(2))^(2^0)+(2-sqrt(2))^(2^0), a(1) = (2+sqrt(2))^(2^1)+(2-sqrt(2))^(2^1); a(2) = (2+sqrt(2))^(2^2)+(2-sqrt(2))^(2^2); etc. %C A152121 For all n the value 2^(n+1) can be factored from each a(n), which except for a different initial term (a(0) = 2 instead of a(0) = 1) matches the sequence A001601 for n>0. %H A152121 Dennis Martin, Table of n, a(n) for n = 0..10 %F A152121 a(n) = a(n-1)^2 - 2^(1+2^(n-1)) %e A152121 a(0) = 4; a(1) = 4^2 - 2^2 = 12; a(2) = 12^2 - 2^3 = 136; a(3) = 136^2 - 2^5 = 18464; a(4) = 18464^2 - 2^9 = 340918784. %Y A152121 Cf. A056236, A001601 %K A152121 easy,nonn %O A152121 0,1 %A A152121 Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 24 2008 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE