A039721 a(1) = 1, a(m+1) = 2*Sum_{k=1..floor((m+1)/2)} a(m+1-k).

1, 2, 4, 12, 32, 96, 280, 840, 2496, 7488, 22400, 67200, 201408, 604224, 1812112, 5436336, 16307328, 48921984, 146760960, 440282880, 1320833664, 3962500992, 11887458176, 35662374528, 106986989184, 320960967552, 962882499840, 2888647499520, 8665941290112

Offset: 1

Author

Leroy Quet, Dec 11 1999

Keywords

• easy
• nonn

Examples

			a(6)=2*(a(5)+a(4)+a(3)) = 2*(32+12+4) = 96.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..212

Crossrefs

Cf. A039722 (similar definition).

Programs

Maple

a[1]:= 1;
for m from 1 to 100 do
   a[m+1]:= 2*add(a[m+1-k],k=1..floor((m+1)/2));
od:
seq(a[i],i=1..100); # Robert Israel, May 18 2014

Mathematica

Fold[Append[#1, 2 Total[#1[[#2 - Range[Floor[#2/2] ] ]] ] ] &, {1}, Range[2, 29]] (* Michael De Vlieger, Dec 11 2017 *)

PARI

lista(nn) = {v = vector(nn); v[1] = 1; for (n=2, nn, v[n] = 2*sum(k=1, n\2, v[n-k]);); v;} \\ Michel Marcus, May 18 2014

Formula

a(1)=1, a(2)=2, a(2m+1)=3*a(2m)-2*a(m), a(2m+2)=3*a(2m+1) (m is positive integer).

Extensions

More terms from James Sellers, May 04 2000

Two more terms from Michel Marcus, May 18 2014