A284565 Bisection of A000360.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Apr 05 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192

Crossrefs

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

Programs

Mathematica

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 *)

Scheme

(define (A284565 n) (A001222 (A284563 n)))
(define (A284565 n) (A000360with_prep_0 (+ n n 1))) ;; See code in A284556.

Formula

a(n) = A000360(2n).

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

Other identities. For all n >= 1:

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