A064657 -id:A064657 - 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

A309494 a(1) = a(2) = a(3) = a(5) = 1, a(4) = 2; a(n) = a(n-a(n-3)) + a(n-a(n-4)) for n > 5.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 3, 5, 8, 8, 7, 5, 2, 5, 13, 12, 18, 3, 5, 6, 4, 23, 21, 9, 5, 2, 5, 26, 14, 31, 3, 5, 6, 4, 36, 34, 9, 5, 2, 5, 39, 14, 44, 3, 5, 6, 4, 49, 47, 9, 5, 2, 5, 52, 14, 57, 3, 5, 6, 4, 62, 60, 9, 5, 2, 5, 65, 14, 70, 3, 5, 6, 4, 75, 73, 9, 5, 2, 5, 78, 14, 83, 3, 5, 6, 4, 88, 86, 9, 5, 2, 5, 91

Offset: 1

Altug Alkan, Aug 04 2019

A well-defined solution sequence for recurrence a(n) = a(n-a(n-3)) + a(n-a(n-4)).

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-1).

Cf. A064657, A244477, A309492.

for n from 1 to 5 do a[n]:= `if`(n=4,2,1) od:
for n from 6 to 100 do a[n]:= a[n-a[n-3]] + a[n-a[n-4]] od:
seq(a[n],n=1..100); # Robert Israel, Aug 07 2019

a[1]=a[2]=a[3]=a[5]=1; a[4]=2; a[n_] := a[n] = a[n - a[n-3]] + a[n - a[n-4]]; Array[a, 93] (* Giovanni Resta, Aug 07 2019 *)

q=vector(100); q[1]=q[2]=q[3]=q[5]=1; q[4]=2; for(n=6, #q, q[n]=q[n-q[n-3]]+q[n-q[n-4]]); q

Vec(x*(1 + x + x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 7*x^10 + 5*x^11 + 2*x^12 + 3*x^13 + 11*x^14 + 10*x^15 + 14*x^16 + x^17 + x^18 - 6*x^20 + 7*x^21 + 5*x^22 - 5*x^23 - 5*x^24 - 2*x^25 - 4*x^26 + x^27 - 9*x^28 - 3*x^29 - 2*x^30 - 3*x^31 - 3*x^32 + x^33 - 2*x^34 - 2*x^36 - 2*x^41) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12)^2) + O(x^80)) \\ Colin Barker, Aug 08 2019

For k > 1,
  a(13*k-9) = 13*k-8,
  a(13*k-8) = 3,
  a(13*k-7) = 5,
  a(13*k-6) = 6,
  a(13*k-5) = 4,
  a(13*k-4) = 13*k-3,
  a(13*k-3) = 13*k-5,
  a(13*k-2) = 9,
  a(13*k-1) = 5,
  a(13*k)   = 2,
  a(13*k+1) = 5,
  a(13*k+2) = 13*k,
  a(13*k+3) = 14.
From Colin Barker, Aug 05 2019: (Start)
G.f.: x*(1 + x + x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 7*x^10 + 5*x^11 + 2*x^12 + 3*x^13 + 11*x^14 + 10*x^15 + 14*x^16 + x^17 + x^18 - 6*x^20 + 7*x^21 + 5*x^22 - 5*x^23 - 5*x^24 - 2*x^25 - 4*x^26 + x^27 - 9*x^28 - 3*x^29 - 2*x^30 - 3*x^31 - 3*x^32 + x^33 - 2*x^34 - 2*x^36 - 2*x^41) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12)^2).
a(n) = 2*a(n-13) - a(n-26) for n > 42.
(End)

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

ARIBAS

Mathematica

Extensions