0,2

The general formula for powers of k integer is a(n)=k^{1/4*[10*n-7-(-1)^n]}+k^{1/4*[10*n-1+(-1)^n]}-a(n-1), with a(0)=1 and where k is an integer value. If we replace k with "i" or "-i", being i=sqrt(-1), we get a periodic complex sequence (period 8).

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jun 27 2007, Table of n, a(n) for n = 0..106

a(n)=2^{1/4*[10*n-7-(-1)^n]}+2^{1/4*[10*n-1+(-1)^n]}-a(n-1), with a(0)=1.

Write powers of 2 in a sort of 3D clockwise spiral. After the initial 1 (2^0) move right till 2^1=2 (pratically only one step); then move down till 2^2=4 (3,4); then left till 2^3=8 (5,6,7,8). When writing number 5 we are in the same column of 1 so 5 is the second number of the sequence. Then move up till 2^4=16. Then move up perpendicularly to the plane till 2^5=32 and again right till 2^6=64. The number 35 is in the sequence because lays in the same line of 1 and 5. The process continue down, left, up, perpendicular, right and so on.

P:=proc(n) local a, i, x, y; a:=1; print(a); for i from 1 by 1 to n do x:=1/4*(10*i-7-(-1)^i); y:=1/4*(10*i-1+(-1)^i); a:=2^x+2^y-a; print(a); od; end: P(100);

Cf. A108981, A001107.

Sequence in context: A000910 A005562 A097872 this_sequence A048515 A085503 A100739

Adjacent sequences: A124790 A124791 A124792 this_sequence A124794 A124795 A124796

easy,nonn

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jun 27 2007