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A297216 a(0)=1; a(1)=1; for n >= 2, a(n) = a(n-A000120(n)) + a(n-1-A023416(n)) 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
for n >= 6, a(n) = k(n) * (a(0) + 3*a(1)).
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.
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
Sequence in context: A079647 A261205 A036451 * A241743 A321729 A180652
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

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Last modified June 25 18:39 EDT 2024. Contains 373707 sequences. (Running on oeis4.)