A064550 - OEIS

%I #21 Dec 05 2022 05:50:53

%S 1,2,4,7,9,12,16,19,23,26,28,33,37,40,46,49,53,58,62,67,71,74,76,85,

%T 89,92,98,103,107,110,120,123,125,132,140,143,147,154,158,163,169,174,

%U 180,185,189,192,194,211,211,212,222,227,227,234,240,241

%N a(1) = 2, a(n)=a(n-1)+2*Q(n)-n, n > 1 where Q = A005185.

%H Reinhard Zumkeller, <a href="/A064550/b064550.txt">Table of n, a(n) for n = 0..10000</a>

%H Roger L. Bagula, <a href="http://victorian.fortunecity.com/carmelita/435/hofstadterintegers.html">A Simulation of a Prime Type of Sequence: The Hofstadter Integers</a> [broken link]

%p A064550 := proc(n) option remember; if n=0 then 1 else A064550(n-1)+2*A005185(n-1)(n) - n; fi; end;

%t q[0] = q[1] = 1;

%t q[n_] := q[n - q[n - 1]] + q[n - q[n - 2]];

%t a[1] = 2;

%t a[n_] := a[n] = a[n - 1] + 2*(q[n] - n/2);

%t Table[ a[n], {n, 1, 70} ]

%o (ARIBAS): function a064550(maxarg: integer); var n,r,rm,q: integer; qar: array; begin qar := alloc(array,maxarg + 1); qar[0] := 1; for n := 1 to maxarg do if n < 2 then q := 1; else q := qar[n - qar[n - 1]] + qar[n - qar[n - 2]]; end; qar[n] := q; if n = 1 then r := 2; else r := rm + round(2*(q - n/2)); end; rm := r; write(r," "); end; end; a064550(65).

%o (Haskell)

%o a064550 n = a064550_list !! n

%o a064550_list = 1 : 2 : zipWith3 (\a q n -> a + 2 * q - n)

%o     (tail a064550_list) (drop 2 a005185_list) [2..]

%o -- _Reinhard Zumkeller_, May 13 2012

%Y Cf. A064551, A064552, A005185.

%K nonn,nice,easy

%O 0,2

%A _Roger L. Bagula_, Oct 08 2001

%E More terms from _Vladeta Jovovic_, _Klaus Brockhaus_ and _Matthew Conroy_, Oct 09 2001