A039722 a(1) = 1, a(m+1) = 2*Sum_{k=1..floor((m+1)/2)} a(k).

1, 2, 2, 6, 6, 10, 10, 22, 22, 34, 34, 54, 54, 74, 74, 118, 118, 162, 162, 230, 230, 298, 298, 406, 406, 514, 514, 662, 662, 810, 810, 1046, 1046, 1282, 1282, 1606, 1606, 1930, 1930, 2390, 2390, 2850, 2850, 3446, 3446, 4042, 4042, 4854, 4854, 5666, 5666, 6694

Offset: 1

Author

Leroy Quet, Dec 11 1999

Keywords

• easy
• nonn

Examples

			a(6) = 2*(a(1)+a(2)+a(3)) = 2*(1+2+2) = 10.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A039721 (similar definition).

Programs

Mathematica

Fold[Append[#1, 2 Total[#1[[Range[Floor[#2/2] ] ]] ] ] &, {1}, Range[2, 52]] (* 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[k]);); v;} \\ Michel Marcus, May 18 2014

Formula

a(1)=1, a(2)=2, a(2m+1)=a(2m), a(2m+2)=a(2m+1)+2a(m+1) {m is a positive integer.}

Extensions

More terms from Michel Marcus, May 18 2014