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

0,3

Comments

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

Links

Table of n, a(n) for n=0..49.

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.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000120, A023416.

Sequence in context: A079647 A261205 A036451 * A241743 A321729 A180652

Adjacent sequences: A297213 A297214 A297215 * A297217 A297218 A297219

Keyword

nonn,base

Author

Ctibor O. Zizka, Dec 27 2017

Extensions

More terms from Michel Marcus, Dec 27 2017

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

Status

approved