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a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 4.
(Formerly M3536)
1

%I M3536 #29 Jul 04 2019 15:46:50

%S 4,17,69,290,1174,4762,20011,84101,340461,1378277,5590589,22676645,

%T 95292383,400440122,1682945112,7072978202,28633110562,115913692522,

%U 469249565698,1899647488730,7705380235154,31254685366922,126775802093906,514230228456026,2160911540495036

%N a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 4.

%C All terms are congruent to 4 mod 13.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Reinhard Zumkeller, <a href="/A005511/b005511.txt">Table of n, a(n) for n = 1..1000</a>

%p a:= proc(n) option remember; `if`(n=1, 4,

%p 1+(t->a(t)*a(n-t))(iquo(n, 2)))

%p end:

%p seq(a(n), n=1..25); # _Alois P. Heinz_, Jul 04 2019

%t a[1]=4; a[n_]:=a[n]=1+a[Floor[n/2]]*a[Ceiling[n/2]]; Table[a[n],{n,1,22}] (* _Jean-François Alcover_, Mar 21 2011 *)

%o (PARI) a(n)=if(n<2,if(n<1,0,4),1+a(floor(n/2))*a(ceil(n/2))) /* _Ralf Stephan_ */

%K nonn,nice

%O 1,1

%A _Colin Mallows_

%E More terms from _Ralf Stephan_, Jan 10 2004