A287654 a(1) = 1, a(2) = a(3) = a(4) = 2; a(n) = a(a(n-1)) + a(a(n-a(n-1)) + a(n-a(n-2))) for n > 4.

1, 2, 2, 2, 4, 4, 4, 4, 6, 8, 8, 6, 8, 8, 8, 8, 10, 14, 16, 12, 14, 14, 14, 16, 16, 16, 16, 14, 16, 16, 16, 16, 20, 26, 24, 24, 24, 24, 24, 24, 28, 28, 22, 28, 30, 30, 28, 30, 32, 32, 32, 32, 30, 32, 32, 32, 32, 32, 32, 30, 32, 32, 32, 32, 40, 52, 48, 42, 44, 44, 44, 42, 44, 44, 44, 44, 52, 60, 46, 54, 56, 48, 54, 56, 48

Offset

1,2

Comments

There are substantial jumps between generations (i.e. a(2^19) = 2^18 and a(2^19 + 1) = 327608). See also scatterplot in links section.

Links

Table of n, a(n) for n=1..85.

Altug Alkan, Scatterplot of a(n)

Index entries for Hofstadter-type sequences

Maple

N:= 2^10: # to get a(1) to a(N)
C[1]:= 1:
C[2]:= 2:
C[3]:= 2:
C[4]:= 2:
for n from 5 to N do
C[n]:= C[C[n-1]] + C[C[n-C[n-1]] + C[n-C[n-2]]];
od:
S:=seq(C[n], n=1..N);

Prog

(Scheme)
;; An implementation of memoization-macro definec can be found for example in: http://oeis.org/wiki/Memoization
(definec (A287654 n) (cond ((= 1 n) n) ((<= n 4) 2) (else (+ (A287654 (A287654 (- n 1))) (A287654 (+ (A287654 (- n (A287654 (- n 1)))) (A287654 (- n (A287654 (- n 2)))))))))) ;; Antti Karttunen, May 31 2017

Crossrefs

Cf. A004001, A005185, A287292, A287707.

Sequence in context: A007614 A289256 A287155 * A355911 A369207 A113402

Adjacent sequences: A287651 A287652 A287653 * A287655 A287656 A287657

Keyword

nonn

Author

Altug Alkan, May 30 2017

Status

approved