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, 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

Offset: 0

Author

Roger L. Bagula, Mar 27 2006

Keywords

• nonn
• look

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

Crossrefs

Cf. A000032, A005185.

Programs

Haskell

a116590 n = a116590_list !! n
a116590_list = 1 : zipWith (+) a005185_list (drop 2 a005185_list)
-- Reinhard Zumkeller, Apr 25 2012

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}]

Formula

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

Extensions

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