A064551 -id:A064551 - cp's OEIS frontend

A064552 a(0) = 1, a(n) = a(n-1) + 2*q(n) - n for n > 0, where q(n) = A064657(n) = q(|n-q(n-3)|) + q(|n-q(n-4)|) for n > 3, q(n) = 1 for n = 0, 1, 2, 3.

1, 2, 2, 1, 1, 4, 14, 31, 43, 44, 38, 31, 45, 56, 94, 105, 95, 96, 106, 109, 111, 140, 142, 171, 173, 174, 202, 229, 253, 232, 206, 187, 223, 210, 296, 271, 291, 360, 366, 451, 461, 468, 470, 477, 477, 534, 564, 567, 575, 532, 534, 589, 569, 622, 622, 693, 689, 640, 602, 567, 679

Offset: 0

Roger L. Bagula, Oct 08 2001

Ill defined beyond n=866. - M. F. Hasler, Aug 28 2012

Jinyuan Wang, Table of n, a(n) for n = 0..866

Cf. A064550, A064551, A064657.

: function qfunc(n: integer): integer; var r: integer; begin if n < 4 then r := 1; else r := qfunc(abs(n - qfunc(n - 3))) + qfunc(abs(n - qfunc( n - 4))); end; return r; end; function a064552(n: integer); var k,r: integer; begin if n = 0 then r := 1; else r := a064552(n - 1) + round(2*(qfunc(n) - n/2)); end; return r; end; for n := 1 to 60 do write(a064552(n)," "); end;.

a[0] = q[0] = q[1] = q[2] = q[3] = 1;
q[n_] := q[n] = q[Abs[n - q[n - 3]]] + q[Abs[n - q[n - 4]]];
a[n_] := a[n] = a[n - 1] + 2*(q[n] - n/2);
Table[a[n], {n, 0, 70} ]

Corrected and extended by Vladeta Jovovic, Matthew Conroy and Klaus Brockhaus, Oct 09 2001

Sequence A064657, and thus the present one, is ill defined beyond n=866. Keyword 'fini' added by M. F. Hasler, Aug 28 2012

A064550 a(1) = 2, a(n)=a(n-1)+2*Q(n)-n, n > 1 where Q = A005185.

Original entry on oeis.org

1, 2, 4, 7, 9, 12, 16, 19, 23, 26, 28, 33, 37, 40, 46, 49, 53, 58, 62, 67, 71, 74, 76, 85, 89, 92, 98, 103, 107, 110, 120, 123, 125, 132, 140, 143, 147, 154, 158, 163, 169, 174, 180, 185, 189, 192, 194, 211, 211, 212, 222, 227, 227, 234, 240, 241

Offset: 0

Roger L. Bagula, Oct 08 2001

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Roger L. Bagula, A Simulation of a Prime Type of Sequence: The Hofstadter Integers [broken link]

Cf. A064551, A064552, A005185.

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);

a064550 n = a064550_list !! n
a064550_list = 1 : 2 : zipWith3 (\a q n -> a + 2 * q - n)
    (tail a064550_list) (drop 2 a005185_list) [2..]
-- Reinhard Zumkeller, May 13 2012

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

q[0] = q[1] = 1;
q[n_] := q[n - q[n - 1]] + q[n - q[n - 2]];
a[1] = 2;
a[n_] := a[n] = a[n - 1] + 2*(q[n] - n/2);
Table[ a[n], {n, 1, 70} ]

More terms from Vladeta Jovovic, Klaus Brockhaus and Matthew Conroy, Oct 09 2001

cp's OEIS Frontend

A064552 a(0) = 1, a(n) = a(n-1) + 2*q(n) - n for n > 0, where q(n) = A064657(n) = q(|n-q(n-3)|) + q(|n-q(n-4)|) for n > 3, q(n) = 1 for n = 0, 1, 2, 3.

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