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a(n+1)=a(n)+a(n-1) if a(n-1) odd, a(n+1)=a(n)+a(n-1)/2 if a(n-1) even.
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%I #8 Dec 23 2022 12:41:55

%S 1,1,2,3,4,7,9,16,25,33,58,91,120,211,271,482,753,994,1747,2244,3991,

%T 5113,9104,14217,18769,32986,51755,68248,120003,154127,274130,428257,

%U 565322,993579,1276240,2269819,2907939,5177758,8085697,10674576

%N a(n+1)=a(n)+a(n-1) if a(n-1) odd, a(n+1)=a(n)+a(n-1)/2 if a(n-1) even.

%H Harvey P. Dale, <a href="/A078696/b078696.txt">Table of n, a(n) for n = 1..1000</a>

%e a(8)=16 even, a(9)=25, so a(10)=25+16/2=25+8=33 a(9)=25 odd, a(10)=33, so a(11)=25+33=58

%t nxt[{a_,b_}]:={b,If[OddQ[a],a+b,a/2+b]}; NestList[nxt,{1,1},40][[All,1]] (* _Harvey P. Dale_, Dec 23 2022 *)

%Y Cf. A000045.

%K easy,nonn

%O 1,3

%A _Miklos Kristof_, Dec 18 2002

%E Corrected by _T. D. Noe_, Oct 25 2006