Dennis Martin, <a href="/A152121/b152121.txt">Table of n, a(n) for n = 0..10</a>

easy,nonn,new

Dennis Martin, <a href="http://www.research.att.com/~njas/sequences/b152121.txt">Table of n, a(n) for n = 0..10</a>

easy,nonn,new

a(0) = 4; for n>0, a(n) = a(n-1)^2 - 2^(1+2^(n-1))

4, 12, 136, 18464, 340918784, 116225617283907584, 13508394113025357323362163662782464, 182476711512818130204254420972394401125552102555370860811711166808064

0,1

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.

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.

Dennis Martin, <a href="http://www.research.att.com/~njas/sequences/b152121.txt">Table of n, a(n) for n = 0..10</a>

a(n) = a(n-1)^2 - 2^(1+2^(n-1))

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.

Cf. A056236, A001601

easy,nonn

Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 24 2008

approved