A064552 -id:A064552 - cp's OEIS frontend

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

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

A064551 Ado [Simone Caramel]'s function: a(0) = 1, a(n) = a(n-1) + 2*(Fibonacci(n+1)-n), n > 0.

Original entry on oeis.org

1, 1, 1, 1, 3, 9, 23, 51, 103, 195, 353, 619, 1061, 1789, 2981, 4925, 8087, 13221, 21547, 35039, 56891, 92271, 149541, 242231, 392233, 634969, 1027753, 1663321, 2691723, 4355745, 7048223, 11404779, 18453871, 29859579, 48314441, 78175075, 126490637, 204666901, 331158797

Offset: 0

Roger L. Bagula, Oct 08 2001

A Pickover sequence with properties analogous to the primes.

Ado [Simone Caramel], Postings in egroups and newsgroups.

T. D. Noe, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

Cf. A000045, A064550, A064552, A065220, A001924.

function a064551(maxarg: integer); var n,r,rm,q,qm1,qm2: integer; begin qm2 := 0; qm1 := 0; rm := 0; for n := 0 to maxarg do if n < 2 then q := 1; else q := qm1 + qm2; end; qm2 := qm1; qm1 := q; if n = 0 then r := 1; else r := rm + 2*(q - n); end; rm := r; write(r," "); end; end; a064551(35);

a064551 n = a064551_list !! n
a064551_list = 1 : zipWith (+) a064551_list
                   (map (* 2) $ zipWith (-) (drop 2 a000045_list) [1..])
-- Reinhard Zumkeller, Sep 13 2013

a:= proc(n) option remember: a(n-1)+2*(combinat[fibonacci](n+1)-n) end: a(0):=1: for n from 0 to 60 do printf(`%d, `, a(n)) od:

a[0] = f[0] = f[1] = 1; f[n_] := f[n] = f[n - 1] + f[n - 2]; a[n_] := a[n] = a[n - 1] + 2*(f[n] - n); Table[ a[n], {n, 0, 40} ]
LinearRecurrence[{4,-5,1,2,-1},{1,1,1,1,3},50] (* Harvey P. Dale, Sep 27 2011 *)

From T. D. Noe, Oct 12 2007: (Start)
G.f.: (1 - 3x + 2x^2 + x^3 + x^4)/((x-1)^3 (x^2 + x - 1)).
a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5). (End)
a(n) = (1/5)*2^(-n)*(-15*2^n + (10-4*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(10+4*sqrt(5))) - n - n^2. - Jean-François Alcover, May 28 2013
a(n) = a(n-1) - 2 * A065220(n), n > 0. - Reinhard Zumkeller, Sep 13 2013
a(n) = 2*F(n+3) - n^2 - n - 3 = 1 + 2*Sum_{k=1..n} F(k+1) - k = 1 + 2*Sum_{k=1..n} A001924(k-3), F=A000045. - Ehren Metcalfe, Dec 27 2018
E.g.f.: 4*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 2*sqrt(5)*sinh(sqrt(5)*x/2))/5 - exp(x)*(3 + x*(2 + x)). - Stefano Spezia, Oct 16 2023

A064714 Define q(0)=1, q(1)=1, q(2)=1, q(n)=q(abs(n-q(n-2)))+q(abs(n-q(n-3))) (A063892); then a(0) = 1, a(n)=a(n-1)+2*(q(n)-n/2), n > 0.

Original entry on oeis.org

1, 2, 2, 3, 7, 14, 18, 17, 15, 24, 26, 23, 25, 36, 40, 35, 33, 36, 50, 63, 63, 66, 68, 77, 81, 98, 98, 105, 93, 92, 110, 131, 137, 128, 110, 121, 129, 138, 124, 119, 115, 130, 158, 167, 155, 154, 176, 223, 219, 182, 152, 173, 259, 278, 266, 261, 271, 296, 304, 303

Offset: 0

Robert G. Wilson v, Oct 13 2001

Cf. A063892, A064552.

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

cp's OEIS Frontend

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

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A064551 Ado [Simone Caramel]'s function: a(0) = 1, a(n) = a(n-1) + 2*(Fibonacci(n+1)-n), n > 0.

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A064714 Define q(0)=1, q(1)=1, q(2)=1, q(n)=q(abs(n-q(n-2)))+q(abs(n-q(n-3))) (A063892); then a(0) = 1, a(n)=a(n-1)+2*(q(n)-n/2), n > 0.

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