OFFSET
1,2
COMMENTS
a(n) = n only for n = 1, 2, 4, 8. These correspond to the four normed division algebras: the real numbers, the complex numbers, the quaternions, and the octonions.
All terms are powers of 2: a(n) = 2^A236916(n-1).
LINKS
John Baez, John Baez on the number 8, 2008 Rankin Lecture (see frame at 38 minutes and 5 seconds).
Index entries for linear recurrences with constant coefficients, signature (2,-2,0,4,-8,8).
FORMULA
a(n) = 16*a(n-8) = 2*a(n-1) - 2*a(n-2) + 4*a(n-4) - 8*a(n-5) + 8*a(n-6).
G.f.: x*(1+2*x^2+4*x^5)/((1-2*x^2)*(1+2*x^2)*(1-2*x+2*x^2)). - Colin Barker, Jan 30 2014
MATHEMATICA
LinearRecurrence[{2, -2, 0, 4, -8, 8}, {1, 2, 4, 4, 4, 4}, 50] (* Harvey P. Dale, May 05 2019 *)
PROG
(PARI) Vec(x*(1+2*x^2+4*x^5)/((1-2*x^2)*(1+2*x^2)*(1-2*x+2*x^2)) + O(x^100)) \\ Colin Barker, Jan 30 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charles R Greathouse IV and William J. Keith, Jan 29 2014
STATUS
approved