OFFSET
0,1
COMMENTS
Shift 2^n+1 left 2n bits.
LINKS
Harry J. Smith, Table of n, a(n) for n=0,...,200
D. Suprijanto and Rusliansyah, Observation on Sums of Powers of Integers Divisible by Four, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, 2219 - 2226.
Index entries for linear recurrences with constant coefficients, signature (12,-32).
FORMULA
G.f.: 1/(1-4*x)+1/(1-8*x). E.g.f.: e^(4*x)+e^(8*x). - Mohammad K. Azarian, Jan 11 2009
a(n)=12*a(n-1)-32*a(n-2) with a(0)=2, a(1)=12. - Vincenzo Librandi, Jul 21 2010
G.f.: G(0), where G(k)= 1 + 2^k/(1 - 4*x/(4*x + 2^k/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 22 2013
EXAMPLE
n=3: 23+1 shifted 2*3 bits to the left is 576 because 23+1 in binary is [1, 0, 0, 1] and 576 is [1, 0, 0, 1, 0, 0, 0, 0, 0, 0].
MATHEMATICA
Table[4^n + 8^n, {n, 0, 25}]
PROG
(PARI) for(n=0, 22, print(shift(2^n+1, 2*n)))
(PARI) { for (n=0, 200, write("b063481.txt", n, " ", shift(1, 2*n) + shift(1, 3*n)) ) } \\ Harry J. Smith, Aug 23 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jul 28 2001
EXTENSIONS
Edited by Robert G. Wilson v, Aug 25 2002
STATUS
approved