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

%I

%S 1,2,4,12,32,96,280,840,2496,7488,22400,67200,201408,604224,1812112,

%T 5436336,16307328,48921984,146760960,440282880,1320833664,3962500992,

%U 11887458176,35662374528,106986989184,320960967552,962882499840,2888647499520,8665941290112

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

%H Robert Israel, <a href="/A039721/b039721.txt">Table of n, a(n) for n = 1..212</a>

%F 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).

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

%p a[1]:= 1;

%p for m from 1 to 100 do

%p a[m+1]:= 2*add(a[m+1-k],k=1..floor((m+1)/2));

%p od:

%p seq(a[i],i=1..100); # _Robert Israel_, May 18 2014

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

%o (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

%Y Cf. A039722 (similar definition).

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Dec 11 1999

%E More terms from _James A. Sellers_, May 04 2000

%E Two more terms from _Michel Marcus_, May 18 2014

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)