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a(1)=a(2)=1, a(n)=a(n-1)+a(n-2) if n is odd, a(n)=a(n-1)+a(n/2) if n is even.
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%I #8 Aug 22 2024 20:55:23

%S 1,1,2,3,5,7,12,15,27,32,59,66,125,137,262,277,539,566,1105,1137,2242,

%T 2301,4543,4609,9152,9277,18429,18566,36995,37257,74252,74529,148781,

%U 149320,298101,298667,596768,597873,1194641,1195778,2390419,2392661

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

%F a(2n) is asymptotic to c*2^n and a(2n+1) to c*2^(n+1) where c=1.14147011562626318730578487228102392422856384213213612463664....

%o (PARI) a(n)=if(n<3,1,a(n-1)+if(n%2,a(n-2),a(n/2)))

%K nonn

%O 1,3

%A _Benoit Cloitre_, Jan 11 2003