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A266569 a(1) = 1; thereafter a(2k) = 4k + a(k); a(2k+1) = k + a(4k+4).

%I A266569 #32 May 06 2016 06:52:02
%S A266569 1,5,30,13,68,42,64,29,132,88,119,66,154,92,132,61,248,168,217,128,
%T A266569 261,163,221,114,322,206,273,148,326,192,268,125,468,316,401,240,463,
%U A266569 293,387,208,533,345,448,251,519,313,425,210,646,422,543,310,623,381,511
%N A266569 a(1) = 1; thereafter a(2k) = 4k + a(k); a(2k+1) = k + a(4k+4).
%H A266569 Daniel Suteu, <a href="/A266569/b266569.txt">Table of n, a(n) for n = 1..10000</a>
%H A266569 Daniel Suteu, <a href="/A266569/a266569.txt">Table of n, a(n) for n = 1..100000</a>
%e A266569 For n=2, a(2) = 4 + a(1) = 5.
%e A266569 For n=3:
%e A266569 a(3) = 1 + a(8);
%e A266569 a(8) = 2*8 + a(8/2) = 16 + a(4);
%e A266569 a(4) = 2*4 + a(4/2) = 8 + a(2) = 13;
%e A266569 a(8) = 18+13 = 29;
%e A266569 a(3) = 1 + 29 = 30.
%p A266569 A266569 := proc(n)
%p A266569     option remember;
%p A266569     local k;
%p A266569     if n = 1 then
%p A266569         1;
%p A266569     elif type(n,'even') then
%p A266569         2*n+procname(n/2) ;
%p A266569     else
%p A266569         k := (n-1)/2 ;
%p A266569         k+procname(4*k+4) ;
%p A266569     end if;
%p A266569 end proc:
%p A266569 seq(A266569(n),n=1..100) ; # _R. J. Mathar_, May 06 2016
%t A266569 a[1] = 1; a[n_] := a[n] = If[EvenQ@ n, 2 n + a[n/2], (n - 1)/2 + a[2 (n + 1)]]; Array[a, 55] (* _Michael De Vlieger_, Jan 02 2016 *)
%o A266569 (Sidef)
%o A266569 func a((1)) { 1 }
%o A266569 func a(n {.is_even}) is cached { 2*n + a(n/2) }
%o A266569 func a(n {.is_odd }) is cached { (n-1)/2 + a(2*(n + 1)) }
%o A266569 1000.times { |n| say a(n) }
%Y A266569 Records (high water marks): A270811, A270812.
%Y A266569 Cf. A270814, A271473, A271478, A271479.
%K A266569 nonn,easy
%O A266569 1,2
%A A266569 _Daniel Suteu_, Jan 01 2016