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A064324 a(n) = a(n-1) + floor(a(n-2)/2) with a(0)=1, a(1)=2.

%I A064324 #23 Jul 28 2023 15:30:35
%S A064324 1,2,2,3,4,5,7,9,12,16,22,30,41,56,76,104,142,194,265,362,494,675,922,
%T A064324 1259,1720,2349,3209,4383,5987,8178,11171,15260,20845,28475,38897,
%U A064324 53134,72582,99149,135440,185014,252734,345241,471608,644228,880032
%N A064324 a(n) = a(n-1) + floor(a(n-2)/2) with a(0)=1, a(1)=2.
%C A064324 a(n)/a(n-1) approaches (1+sqrt(3))/2 = 1.3660254... = A332133 for large n.
%H A064324 Harry J. Smith, <a href="/A064324/b064324.txt">Table of n, a(n) for n = 0..400</a>
%F A064324 a(n) = A064323(n) + 1.
%e A064324 a(5) = a(4)+floor(a(3)/2) = 4+floor(3/2) = 5.
%t A064324 RecurrenceTable[{a[n] == a[n-1] + Floor[a[n-2]/2], a[0] == 1, a[1] == 2}, a, {n, 0, 50}] (* _G. C. Greubel_, May 04 2019 *)
%t A064324 nxt[{a_,b_}]:={b,Floor[a/2]+b}; NestList[nxt,{1,2},50][[;;,1]] (* _Harvey P. Dale_, Jul 28 2023 *)
%o A064324 (PARI) { for (n=0, 400, if (n>1, a=a1 + a2\2; a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b064324.txt", n, " ", a) ) }; \\ _Harry J. Smith_, Sep 11 2009
%o A064324 (Magma) [n le 2 select n else Self(n-1)+Floor(Self(n-2)/2): n in [1..45]]; // _Bruno Berselli_, Apr 20 2012
%Y A064324 Cf. A064323, A332133, A182229, A182230.
%K A064324 nonn
%O A064324 0,2
%A A064324 _Henry Bottomley_, Sep 11 2001