cp's OEIS Frontend

A078446 a(1)=a(2)=1; a(n)=a(n-2)/2 if a(n-2) is even, a(n)=a(n-1)+a(n-2) otherwise.

%I A078446 #15 Jul 18 2025 16:58:27
%S A078446 1,1,2,3,1,4,5,2,7,1,8,9,4,13,2,15,1,16,17,8,25,4,29,2,31,1,32,33,16,
%T A078446 49,8,57,4,61,2,63,1,64,65,32,97,16,113,8,121,4,125,2,127,1,128,129,
%U A078446 64,193,32,225,16,241,8,249,4,253,2,255,1,256,257,128,385,64,449,32,481,16,497
%N A078446 a(1)=a(2)=1; a(n)=a(n-2)/2 if a(n-2) is even, a(n)=a(n-1)+a(n-2) otherwise.
%C A078446 The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446. - _Jeremy Gardiner_, Mar 16 2003
%H A078446 G. C. Greubel, <a href="/A078446/b078446.txt">Table of n, a(n) for n = 1..1000</a>
%F A078446 a(n^2)=2^n-1; a(n^2+1)=1; a(n^2+2)=2^n; a(n^2+3)=2^n+1; a(n^2+4)=2^(n-1); a(n^2+5)=3*2^n+1 ...; inequality : a(n)/2^sqrt(n) <2
%F A078446 Sum(k=1, n^2, a(k)) = 2*(n-2)*2^n + n*(n+1)/2 + 4
%p A078446 a:= proc(n) option remember;
%p A078446       if n < 3 then 1
%p A078446     elif `mod`(procname(n-2), 2) = 0 then procname(n-2)/2
%p A078446     else procname(n-1) + procname(n-2)
%p A078446       fi
%p A078446     end:
%p A078446 seq(a(n), n=1..80); # _G. C. Greubel_, Nov 07 2019
%t A078446 a[n_]:= a[n]= If[n<3, 1, If[EvenQ[a[n-2]], a[n-2]/2, a[n-1]+a[n-2]]];
%t A078446 Table[a[n], {n, 80}] (* _G. C. Greubel_, Nov 07 2019 *)
%t A078446 nxt[{a_,b_}]:={b,If[EvenQ[a],a/2,a+b]}; NestList[nxt,{1,1},80][[;;,1]] (* _Harvey P. Dale_, Jul 18 2025 *)
%o A078446 (PARI) a(n) = if(n<3, 1, if(a(n-2)%2==0, a(n-2)/2, a(n-1) + a(n-2) )); \\ _G. C. Greubel_, Nov 07 2019
%o A078446 (Sage)
%o A078446 @CachedFunction
%o A078446 def a(n):
%o A078446     if (n<3): return 1
%o A078446     elif (a(n-2)%2==0): return a(n-2)/2
%o A078446     else: return a(n-1) + a(n-2)
%o A078446 [a(n) for n in (1..80)] # _G. C. Greubel_, Nov 07 2019
%K A078446 nonn
%O A078446 1,3
%A A078446 _Benoit Cloitre_, Dec 31 2002