A064550 -id:A064550 - 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

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

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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