login
Bisection of A000360.
5

%I #11 Oct 13 2017 00:31:59

%S 1,1,1,2,2,2,3,2,2,4,4,3,4,4,3,3,3,4,6,5,5,7,6,4,5,6,6,6,5,5,5,3,3,6,

%T 7,6,8,9,8,7,7,9,11,9,8,10,8,5,6,8,9,9,9,10,10,7,6,9,9,7,7,7,5,4,4,6,

%U 9,8,9,12,11,8,10,13,14,13,12,13,12,8,8,13,15,13,15,17,15,12,11,14,16,13,11,13,10,6,7,10

%N Bisection of A000360.

%H Antti Karttunen, <a href="/A284565/b284565.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) = A000360(2n).

%F a(n) = A001222(A284563(n)).

%F Other identities. For all n >= 1:

%F A007306(n) = a(n-1) + A284566(n-1).

%t a[n_] := a[n] = Which[n == 0, 1, EvenQ@ n, a[n/2] + a[n/2 - 1], True, a[(n - 1)/2] - Mod[(n - 1)/2 - 1, 3] + 1]; Table[a[2 n], {n, 0, 97}] (* _Michael De Vlieger_, Apr 05 2017, after _Jean-François Alcover_ at A000360 *)

%o (Scheme)

%o (define (A284565 n) (A001222 (A284563 n)))

%o (define (A284565 n) (A000360with_prep_0 (+ n n 1))) ;; See code in A284556.

%Y Cf. A000360, A001222, A007306, A284556, A284563, A284566.

%K nonn

%O 0,4

%A _Antti Karttunen_, Apr 05 2017