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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 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

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