A297216 a(0)=1; a(1)=1; for n >= 2, a(n) = a(n-A000120(n)) + a(n-1-A023416(n)).

1, 1, 2, 3, 4, 6, 8, 12, 16, 20, 28, 36, 48, 64, 84, 120, 156, 184, 240, 312, 396, 480, 624, 792, 1020, 1248, 1584, 2040, 2496, 3288, 4080, 5664, 7248, 8160, 10536, 12912, 16200, 18696, 23448, 29112, 36360, 42144, 52560, 65472, 78504, 94704, 118032, 147264, 183504, 212736

Offset: 0

Author

Ctibor O. Zizka, Dec 27 2017

Keywords

• nonn
• base

Comments

for n >= 6, a(n) = k(n) * (a(0) + 3*a(1)).

Examples

			n=7, A000120(7)=3, A023416(7)=0. a(7) = a(4)+a(6) = a(3)+a(1)+a(4)+a(4) = 3*(a(3)+a(1)) = 3*(a(1)+a(2)+a(1)) = 3*(a(0)+3*a(1)). a(7)=12; k(7)=3.
		

Links

• B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), Article 07.7.1.
• Nathaniel D. Emerson, A Family of Meta-Fibonacci Sequences Defined by Variable-Order Recursions, J. Integer Sequences, Vol. 9 (2006), Article 06.1.8.

Crossrefs

Cf. A000120, A023416.

Programs

Maple

A297216 := proc(n)
    option remember ;
    if n <=1 then
        1;
    else
        procname(n-wt(n))+procname(n-1-A023416(n)) ;
    end if;
end proc:
seq(A297216(n),n=0..30) ; # R. J. Mathar, Jun 19 2021

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = a[n - DigitCount[n, 2, 1]] + a[n - 1 - DigitCount[n, 2, 0]]; Array[a, 50, 0] (* Amiram Eldar, Aug 01 2023 *)

PARI

a(n) = if (n<=1, 1, a(n-hammingweight(n)) + a(n-1-(#binary(n)-hammingweight(n)))); \\ Michel Marcus, Dec 27 2017

Extensions

More terms from Michel Marcus, Dec 27 2017

Offset corrected by R. J. Mathar, Jun 19 2021