A181175 The "Fi1" sums of the powers-of-2 triangle A000079.

1, 2, 40, 320, 21504, 688128, 178257920, 22817013760, 23433341566976, 11997870882291712, 49179307930885816320, 100719222642454151823360, 1650485975228872480767606784, 13520781109074923362448234774528

Offset: 0

Author

Johannes W. Meijer, Oct 10 2010

Keywords

• easy
• nonn

Comments

The a(n) represent the Fi1(n) sums, see A180662, of the powers-of-2 triangle A000079. We observe that Fi2(2*n) = Fi1(2*n) and Fi2(2*n+1) = 2*Fi1(2*n+1).

Programs

Maple

nmax:=13: a(0):=1: a(1):=2: for n from 0 to nmax/2 do a(2*n+1):= 2^(2*n+1)*a(2*n): a(2*n+2):=2^(2*n+2)*((4^(n+2) - 1)/(4^(n+1) - 1))*a(2*n+1): od: seq(a(n),n=0..nmax);

Formula

a(2*n+1) = 2^(2*n+1)*a(2*n) and a(2*n+2) = 2^(2*n+2)*((4^(n+2) - 1)/(4^(n+1) - 1))*a(2*n+1) with a(0) = 1 and a(1) =2.