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A116590 a(0)=1; a(n)=b(n+2)+b(n), where b(n)=A005185(n) is the Hofstadter Q-sequence: b(1)=b(2)=1; b(n)=b(n-b(n-1))+b(n-b(n-2)) for n > 2. 1
1, 3, 4, 5, 7, 8, 9, 11, 11, 12, 14, 14, 16, 18, 17, 20, 20, 21, 23, 23, 24, 24, 28, 26, 30, 30, 30, 32, 32, 36, 33, 37, 37, 38, 39, 41, 41, 41, 44, 44, 45, 47, 47, 48, 48, 48, 56, 48, 57, 54, 53, 56, 58, 56, 58, 62, 58, 64, 62, 64, 64, 72, 65, 71, 71, 66, 71, 74, 73, 76, 78, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = A005185(n+2) + A005185(n) for n>=1.

MAPLE

b:=proc(n) option remember; if n<=2 then 1 else b(n-b(n-1))+b(n-b(n-2)): fi: end: a[0]:=1: for n from 1 to 71 do a[n]:=b(n)+b(n+2) od: seq(a[n], n=0..71);

MATHEMATICA

F[0] = 0; F[1] = 1; F[2] = 1; F[n_] := F[n] = F[n - F[n - 1]] + F[n - F[n - 2]] L[0] = 1; L[n_] := L[n] = F[n - 1] + F[n + 1]

Table[L[n], {n, 1, 200}]

PROG

(Haskell)

a116590 n = a116590_list !! n

a116590_list = 1 : zipWith (+) a005185_list (drop 2 a005185_list)

-- Reinhard Zumkeller, Apr 25 2012

CROSSREFS

Cf. A000032, A005185.

Sequence in context: A169757 A051374 A225048 * A024355 A194413 A183574

Adjacent sequences:  A116587 A116588 A116589 * A116591 A116592 A116593

KEYWORD

nonn,look

AUTHOR

Roger L. Bagula, Mar 27 2006

EXTENSIONS

Edited by N. J. A. Sloane, Apr 15 2006

STATUS

approved

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Last modified June 20 13:02 EDT 2021. Contains 345164 sequences. (Running on oeis4.)