A244477 -id:A244477 - cp's OEIS frontend

A283880 A linear-recurrent solution to Hofstadter's Q recurrence.

12, 6, 4, 6, 1, 6, 12, 10, 4, 6, 13, 6, 12, 16, 4, 6, 25, 6, 12, 26, 4, 6, 37, 6, 12, 42, 4, 6, 49, 6, 12, 68, 4, 6, 61, 6, 12, 110, 4, 6, 73, 6, 12, 178, 4, 6, 85, 6, 12, 288, 4, 6, 97, 6, 12, 466, 4, 6, 109, 6, 12, 754, 4, 6, 121, 6, 12, 1220, 4, 6, 133, 6, 12, 1974, 4

Offset: 1

Nathan Fox, Mar 19 2017

nonn

a(n) is the solution to the recurrence relation a(n) = a(n-a(n-1)) + a(n-a(n-2)) [Hofstadter's Q recurrence], with the initial conditions: a(n) = 0 if n <= 0; a(1) = 12, a(2) = 6, a(3) = 4, a(4) = 6, a(5) = 1, a(6) = 6, a(7) = 12, a(8) = 10, a(9) = 4.

This sequence is an interleaving of six simpler sequences. Four are constant, one is a linear polynomial, and one is a Fibonacci-like sequence.

Nathan Fox, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1).

Cf. A005185, A188670, A244477, A269328, A275153, A283881.

A283880:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 12: elif n = 2 then 6: elif n = 3 then 4: elif n = 4 then 6: elif n = 5 then 1: elif n = 6 then 6: elif n = 7 then 12: elif n = 8 then 10: elif n = 9 then 4: else A283880(n-A283880(n-1)) + A283880(n-A283880(n-2)): fi: end:

from functools import cache
@cache
def a(n):
    if n <= 0: return 0
    if n <= 9: return [12, 6, 4, 6, 1, 6, 12, 10, 4][n-1]
    return a(n - a(n-1)) + a(n - a(n-2))
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Dec 06 2021

a(6n) = 6, a(6n+1) = 12, a(6n+2) = 2*F(n+4), a(6n+3) = 4, a(6n+4) = 6, a(6n+5) = 12n+1.
G.f.: (-6*x^23+11*x^22-6*x^21-4*x^20-4*x^19-12*x^18+12*x^16+2*x^13 +12*x^11 -10*x^10 +12*x^9+8*x^8 +8*x^7+24*x^6-6*x^5-x^4-6*x^3-4*x^2 -6*x-12) / ((-1+x^6+x^12) *(-1+x)^2*(1+x)^2*(1+x+x^2)^2*(1-x+x^2)^2).
a(n) = 3*a(n-6) - 2*a(n-12) - a(n-18) + a(n-24) for n > 24.

A283881 A linear-recurrent solution to Hofstadter's Q recurrence.

Original entry on oeis.org

7, 0, 8, 7, 7, 8, 4, 7, 7, 16, 7, 7, 16, 4, 7, 14, 24, 7, 7, 32, 4, 7, 21, 32, 7, 7, 64, 4, 7, 28, 40, 7, 7, 128, 4, 7, 35, 48, 7, 7, 256, 4, 7, 42, 56, 7, 7, 512, 4, 7, 49, 64, 7, 7, 1024, 4, 7, 56, 72, 7, 7, 2048, 4, 7, 63, 80, 7, 7, 4096, 4, 7, 70, 88, 7, 7

Offset: 1

Nathan Fox, Mar 19 2017

nonn

a(n) is the solution to the recurrence relation a(n) = a(n-a(n-1)) + a(n-a(n-2)) [Hofstadter's Q recurrence], with the initial conditions: a(n) = 0 if n <= 0; a(1) = 7, a(2) = 0, a(3) = 8, a(4) = 7, a(5) = 7, a(6) = 8, a(7) = 4.

This sequence is an interleaving of seven simpler sequences. Four are constant, two are linear polynomials, and one is a geometric sequence.

Nathan Fox, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 2).

Cf. A005185, A188670, A244477, A269328, A275153, A283880.

A283881:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 7: elif n = 2 then 0: elif n = 3 then 8: elif n = 4 then 7: elif n = 5 then 7: elif n = 6 then 8: elif n = 7 then 4: else A283881(n-A283881(n-1)) + A283881(n-A283881(n-2)): fi: end:

a(7n) = 4, a(7n+1) = 7, a(7n+2) = 7n, a(7n+3) = 8n+8, a(7n+4) = 7, a(7n+5) = 7, a(7n+6) = 2^(n+3).
G.f.: (-8*x^20-8*x^19-14*x^18-14*x^17+14*x^15-14*x^14+12*x^13 +16*x^12 +21*x^11 +21*x^10+16*x^9-7*x^8+21*x^7-4*x^6-8*x^5-7*x^4-7*x^3 -8*x^2-7) / ((-1+2*x^7)*(-1+x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)^2).
a(n) = 4*a(n-7) - 5*a(n-14) + 2*a(n-21) for n > 21.

A289205 a(1) = a(2) = a(3) = 1, a(4) = 3; a(n) = n - a(n-a(n-1)) - a(n-a(n-2)) for n > 4.

Original entry on oeis.org

1, 1, 1, 3, 1, 4, 2, 1, 6, 1, 9, 2, 1, 11, 1, 14, 2, 1, 16, 1, 19, 2, 1, 21, 1, 24, 2, 1, 26, 1, 29, 2, 1, 31, 1, 34, 2, 1, 36, 1, 39, 2, 1, 41, 1, 44, 2, 1, 46, 1, 49, 2, 1, 51, 1, 54, 2, 1, 56, 1, 59, 2, 1, 61, 1, 64, 2, 1, 66, 1, 69, 2, 1, 71, 1, 74, 2, 1, 76, 1, 79, 2, 1, 81, 1, 84, 2, 1, 86, 1, 89, 2, 1, 91, 1, 94, 2, 1, 96, 1, 99, 2, 1, 101

Offset: 1

Altug Alkan, Jun 28 2017

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Cf. A244477.

LinearRecurrence[{0,0,0,0,2,0,0,0,0,-1},{1,1,1,3,1,4,2,1,6,1,9,2,1,11},120] (* Harvey P. Dale, Aug 20 2017 *)

q=vector(10^5); q[1]=q[2]=q[3]=1;q[4]=3; for(n=5, #q, q[n] = n-q[n-q[n-1]]-q[n-q[n-2]]); q

Vec(x*(1 + x)*(1 + x^2 + 2*x^3 - x^4 + 3*x^5 - 3*x^6 + 2*x^7 - 2*x^8 + x^9 + x^10 - 2*x^11 + 2*x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2) + O(x^100)) \\ Colin Barker, Jun 28 2017

a(5k) = a(5k + 3) = 1, a(5k + 1) = 5k - 1, a(5k + 2) = 2, a(5k + 4) = 5k + 1 for k > 0.
From Colin Barker, Jun 28 2017: (Start)
G.f.: x*(1 + x)*(1 + x^2 + 2*x^3 - x^4 + 3*x^5 - 3*x^6 + 2*x^7 - 2*x^8 + x^9 + x^10 - 2*x^11 + 2*x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).
a(n) = 2*a(n-5) - a(n-10) for n>12.
(End)

A296786 a(1) = a(2) = a(5) = 2, a(3) = 1, a(4) = 3, a(6) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 6.

Original entry on oeis.org

2, 2, 1, 3, 2, 5, 7, 8, 7, 4, 11, 12, 11, 4, 15, 16, 15, 4, 19, 20, 19, 4, 23, 24, 23, 4, 27, 28, 27, 4, 31, 32, 31, 4, 35, 36, 35, 4, 39, 40, 39, 4, 43, 44, 43, 4, 47, 48, 47, 4, 51, 52, 51, 4, 55, 56, 55, 4, 59, 60, 59, 4, 63, 64, 63, 4, 67, 68, 67, 4, 71, 72, 71, 4, 75, 76, 75, 4, 79, 80, 79, 4

Offset: 1

Altug Alkan, Dec 20 2017

A quasi-periodic solution to the three-term Hofstadter recurrence a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)). See comments in A296518.

Colin Barker, Table of n, a(n) for n = 1..1000
Altug Alkan, On a conjecture about generalized Q-recurrence, Open Mathematics (2018) Vol. 16, Issue 1, 1490-1500.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Cf. A005185, A244477, A268368, A278055, A296413, A296440, A296518, A296690.

a:= proc(n) option remember; procname(n-procname(n-1))+procname(n-procname(n-2))+procname(n-procname(n-3)) end proc:
a(1):= 2: a(2):= 2: a(3):= 1: a(4):= 3: a(5):= 2: a(6):= 5:
map(a, [$1..100]); # after Robert Israel at A296440

a[n_] := a[n] = If[n<7, {2, 2, 1, 3, 2, 5}[[n]], a[n - a[n-1]] + a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 100] (* after Giovanni Resta at A296440 *)

q=vector(10^5); q[1]=2;q[2]=2;q[3]=1;q[4]=3;q[5]=2;q[6]=5;for(n=7, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q

Vec(x*(2 + 2*x + x^2 + 3*x^3 - 2*x^4 + x^5 + 5*x^6 + 2*x^7 + 5*x^8 - 4*x^9 - 2*x^10 - x^11 - x^12 + x^13) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2) + O(x^100)) \\ Colin Barker, Dec 29 2017

a(4*k-1) = a(4*k+1) = 4*k-1, a(4*k) = 4*k, a(4*k+2) = 4, for k > 1.
From Colin Barker, Dec 28 2017: (Start)
G.f.: x*(2 + 2*x + x^2 + 3*x^3 - 2*x^4 + x^5 + 5*x^6 + 2*x^7 + 5*x^8 - 4*x^9 - 2*x^10 - x^11 - x^12 + x^13) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>14.
(End)

A275365 a(1)=2, a(2)=2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

Original entry on oeis.org

0, 2, 2, 4, 2, 6, 2, 8, 2, 10, 2, 12, 2, 14, 2, 16, 2, 18, 2, 20, 2, 22, 2, 24, 2, 26, 2, 28, 2, 30, 2, 32, 2, 34, 2, 36, 2, 38, 2, 40, 2, 42, 2, 44, 2, 46, 2, 48, 2, 50, 2, 52, 2, 54, 2, 56, 2, 58, 2, 60, 2, 62, 2, 64, 2, 66, 2, 68, 2, 70, 2, 72, 2, 74

Offset: 0

Nathan Fox, Jul 24 2016

a(n) is the solution to the recurrence relation a(n) = a(n-a(n-1)) + a(n-a(n-2)) [Hofstadter's Q recurrence], with the initial conditions: a(n) = 0 if n <= 0; a(1) = 2, a(2) = 2.
Starting with n=1, a(n) is A005843 interleaved with A007395.
This sequence is the same as A133265 with the leading 2 changed to a 0.

Nathan Fox, Table of n, a(n) for n = 0..1000
Nathan Fox, Finding Linear-Recurrent Solutions to Hofstadter-Like Recurrences Using Symbolic Computation, arXiv:1609.06342 [math.NT], 2016.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A005185, A133265, A188670, A244477, A264756, A264757, A264758, A268368, A275153, A275361, A275362.

Join[{0}, LinearRecurrence[{0, 2, 0, -1}, {2, 2, 4, 2}, 73]] (* Jean-François Alcover, Feb 19 2019 *)

a(0) = 0; thereafter, a(2n) = 2, a(2n+1) = 2n+2.
a(n) = 2*a(n-2) - a(n-4) for n>4.
G.f.: -(2*x^3 -2*x -2)/((x-1)^2*(x+1)^2).

A283904 Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 1; thereafter a(n) = a(n-2a(n-1)) + a(n-3a(n-2)).

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 3, 3, 1, 4, 4, 2, 2, 7, 2, 2, 6, 3, 3, 11, 2, 3, 12, 2, 2, 14, 2, 2, 14, 3, 2, 14, 4, 14, 15, 1, 15, 18, 1, 18, 20, 1, 20, 22, 1, 22, 23, 1, 23, 25, 1, 25, 26, 1, 26, 28, 1, 28, 29, 1, 29, 31, 1, 31, 32, 1, 32, 34, 1, 34, 35, 1, 35, 37, 1

Offset: 1

Nathan Fox, Mar 19 2017

nonn

This sequence is eventually quasilinear with period 6. Each component sequence has slope 0 or 1/2.

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

Cf. A005185, A188670, A244477.

A283904:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: else A283904(n-2*A283904(n-1)) + A283904(n-3*A283904(n-2)): fi: end:

If the index is at least 41:
a(6n) = 1
a(6n+1) = 3n-1
a(6n+2) = 3n+1
a(6n+3) = 1
a(6n+4) = 3n+1
a(6n+5) = 3n+2.
G.f.: (-x^48-x^46-x^45-x^43+x^42+3*x^41+x^40-9*x^39-x^38+3*x^37+x^36-4*x^35+x^34+12*x^33+x^32-2*x^31+x^30+x^29-x^28+x^26-3*x^25-2*x^24-x^23+2*x^22-x^20+2*x^19+3*x^18-2*x^16-x^15+2*x^13-3*x^12+x^11-x^8+x^4+x^3+x^2+x+1) / ((1+x)*(1-x+x^2)*(-1+x)^2*(1+x+x^2)^2).
a(n) = a(n-3) + a(n-6) - a(n-9) for n > 49.

A284429 A quasilinear solution to Hofstadter's Q recurrence.

Original entry on oeis.org

2, 1, 3, 5, 1, 3, 8, 1, 3, 11, 1, 3, 14, 1, 3, 17, 1, 3, 20, 1, 3, 23, 1, 3, 26, 1, 3, 29, 1, 3, 32, 1, 3, 35, 1, 3, 38, 1, 3, 41, 1, 3, 44, 1, 3, 47, 1, 3, 50, 1, 3, 53, 1, 3, 56, 1, 3, 59, 1, 3, 62, 1, 3, 65, 1, 3, 68, 1, 3, 71, 1, 3, 74, 1, 3

Offset: 1

Nathan Fox, Mar 26 2017

a(n) is the solution to the recurrence relation a(n) = a(n-a(n-1)) +a(n-a(n-2)) [Hofstadter's Q recurrence], with the initial conditions: a(1) = 2, a(2) = 1.

This sequence is a close relative of A283878.

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

Cf. A005185, A188670, A244477, A264756, A283878, A283879.

A284429:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 2: elif n = 2 then 1: else A284429(n-A284429(n-1)) + A284429(n-A284429(n-2)): fi: end:

CoefficientList[Series[(-3*x^5 - x^4 + x^3 + 3*x^2 + x + 2) / ((-1 + x)^2*(1 + x + x^2)^2), {x, 0, 100}], x] (* Indranil Ghosh, Mar 27 2017 *)

Vec((-3*x^5 - x^4 + x^3 + 3*x^2 + x + 2) / ((-1 + x)^2*(1 + x + x^2)^2) + O(x^100)) \\ Indranil Ghosh, Mar 27 2017

G.f.: (-3*x^5 - x^4 + x^3 + 3*x^2 + x + 2) / ((-1 + x)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-3) - a(n-6) for n > 6.
a(3*k)   = 3,
a(3*k+1) = 3*k+2,
a(3*k+2) = 1.

A296337 a(1) = a(3) = 1, a(2) = 2, a(4) = a(5) = 4; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 5.

Original entry on oeis.org

1, 2, 1, 4, 4, 4, 2, 8, 3, 4, 10, 10, 2, 14, 3, 4, 16, 16, 2, 20, 3, 4, 22, 22, 2, 26, 3, 4, 28, 28, 2, 32, 3, 4, 34, 34, 2, 38, 3, 4, 40, 40, 2, 44, 3, 4, 46, 46, 2, 50, 3, 4, 52, 52, 2, 56, 3, 4, 58, 58, 2, 62, 3, 4, 64, 64, 2, 68, 3, 4, 70, 70, 2, 74, 3, 4, 76, 76, 2, 80, 3, 4, 82, 82

Offset: 1

Altug Alkan, Dec 10 2017

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

Cf. A244477.

Fold[Append[#1, #1[[#2 - #1[[#2 - 1]] ]] + #1[[#2 - #1[[#2 - 2]] ]] ] &, {1, 2, 1, 4, 4}, Range[6, 84]] (* Michael De Vlieger, Dec 11 2017 *)

q=vector(10^5); q[1]=1;q[2]=2;q[3]=1;q[4]=4;q[5]=4;for(n=6, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]); q

Vec(x*(1 + 2*x + x^2 + 4*x^3 + 4*x^4 + 4*x^5 + 4*x^7 + x^8 - 4*x^9 + 2*x^10 + 2*x^11 - x^12 - 2*x^14) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2) + O(x^40)) \\ Colin Barker, Dec 11 2017

a(6*k + 1) = 2, a(6*k - 4) = 6*k - 4, a(6*k + 3) = 3, a(6*k - 2) = 4, a(6*k - 1) = a(6*k) = 6*k - 2 for k >= 1. - Iain Fox, Dec 10 2017
From Colin Barker, Dec 11 2017: (Start)
G.f.: x*(1 + 2*x + x^2 + 4*x^3 + 4*x^4 + 4*x^5 + 4*x^7 + x^8 - 4*x^9 + 2*x^10 + 2*x^11 - x^12 - 2*x^14) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-6) - a(n-12) for n>13.
(End)

A302130 a(n) = a(a(n-3)) + a(n-a(n-2)) with a(1) = a(2) = a(3) = a(4) = 1, a(5) = 2, a(6) = 5.

Original entry on oeis.org

1, 1, 1, 1, 2, 5, 3, 2, 7, 3, 2, 10, 3, 2, 13, 3, 2, 16, 3, 2, 19, 3, 2, 22, 3, 2, 25, 3, 2, 28, 3, 2, 31, 3, 2, 34, 3, 2, 37, 3, 2, 40, 3, 2, 43, 3, 2, 46, 3, 2, 49, 3, 2, 52, 3, 2, 55, 3, 2, 58, 3, 2, 61, 3, 2, 64, 3, 2, 67, 3, 2, 70, 3, 2, 73, 3, 2, 76, 3, 2, 79, 3, 2, 82, 3, 2, 85, 3, 2, 88

Offset: 1

Altug Alkan, Jun 20 2018

A quasi-periodic solution to the recurrence a(n) = a(a(n-3)) + a(n-a(n-2)).

			a(3*k-2) = 3, a(3*k-1) = 2, a(3*k) = 3*k - 2 for k > 2.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Cf. A244477.

a:=[1,1,1,1,2,5];; for n in [7..100] do a[n]:=a[a[n-3]]+a[n-a[n-2]]; od; a; # Muniru A Asiru, Jun 26 2018

LinearRecurrence[{0,0,2,0,0,-1},{1,1,1,1,2,5,3,2,7,3,2,10},100] (* Harvey P. Dale, Apr 20 2022 *)

a=vector(99); a[1]=a[2]=a[3]=a[4]=1;a[5]=2;a[6]=5;for(n=7, #a, a[n] = a[a[n-3]]+a[n-a[n-2]]); a

Vec(x*(1 + x + x^2 - x^3 + 3*x^5 + 2*x^6 - x^7 - 2*x^8 - 2*x^9 + x^11) / ((1 - x)^2*(1 + x + x^2)^2) + O(x^80)) \\ Colin Barker, Jun 20 2018

From Colin Barker, Jun 20 2018: (Start)
G.f.: x*(1 + x + x^2 - x^3 + 3*x^5 + 2*x^6 - x^7 - 2*x^8 - 2*x^9 + x^11) / ((1 - x)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-3) - a(n-6) for n>10.
(End)

A302551 a(n) = a(a(n-1)) + a(n-a(n-2)) with a(1) = a(2) = a(5) = 1, a(3) = a(6) = 2, a(4) = 6.

Original entry on oeis.org

1, 1, 2, 6, 1, 2, 3, 4, 8, 6, 4, 8, 12, 10, 8, 6, 10, 14, 18, 16, 8, 6, 10, 20, 24, 22, 8, 6, 10, 26, 30, 28, 8, 6, 10, 32, 36, 34, 8, 6, 10, 38, 42, 40, 8, 6, 10, 44, 48, 46, 8, 6, 10, 50, 54, 52, 8, 6, 10, 56, 60, 58, 8, 6, 10, 62, 66, 64, 8, 6, 10, 68, 72, 70, 8, 6, 10, 74, 78, 76, 8, 6, 10

Offset: 1

Altug Alkan, Jun 20 2018

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1,0,1,-1,0,1,-1).

Cf. A244477.

a:=[1,1,2,6,1,2];; for n in [7..100] do a[n]:=a[a[n-1]]+a[n-a[n-2]]; od; a; # Muniru A Asiru, Jun 26 2018

a=vector(99); a[1]=1;a[2]=1;a[3]=2;a[4]=6;a[5]=1;a[6]=2;for(n=7, #a, a[n] = a[a[n-1]]+a[n-a[n-2]]); a

Vec(x*(1 + x^2 + 5*x^3 - 5*x^4 + 2*x^5 + 4*x^6 - 4*x^7 + 4*x^8 - 6*x^9 + 4*x^10 + 6*x^11 - 3*x^12 - 3*x^14 + 3*x^15 + 3*x^16 - 6*x^17 + 6*x^19 - 6*x^20) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)) + O(x^80)) \\ Colin Barker, Jun 20 2018

a(6*k-3) = 8, a(6*k-2) = 6, a(6*k-1) = 10, a(6*k) = 6*k - 4, a(6*k+1) = 6*k, a(6*k + 2) = 6*k - 2 for k > 2.
From Colin Barker, Jun 20 2018: (Start)
G.f.: x*(1 + x^2 + 5*x^3 - 5*x^4 + 2*x^5 + 4*x^6 - 4*x^7 + 4*x^8 - 6*x^9 + 4*x^10 + 6*x^11 - 3*x^12 - 3*x^14 + 3*x^15 + 3*x^16 - 6*x^17 + 6*x^19 - 6*x^20) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)).
a(n) = a(n-1) - a(n-3) + a(n-4) + a(n-6) - a(n-7) + a(n-9) - a(n-10) for n>13.
(End)

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A283880 A linear-recurrent solution to Hofstadter's Q recurrence.

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A283881 A linear-recurrent solution to Hofstadter's Q recurrence.

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A289205 a(1) = a(2) = a(3) = 1, a(4) = 3; a(n) = n - a(n-a(n-1)) - a(n-a(n-2)) for n > 4.

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A296786 a(1) = a(2) = a(5) = 2, a(3) = 1, a(4) = 3, a(6) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 6.

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A275365 a(1)=2, a(2)=2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

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A283904 Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 1; thereafter a(n) = a(n-2a(n-1)) + a(n-3a(n-2)).

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A284429 A quasilinear solution to Hofstadter's Q recurrence.

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A296337 a(1) = a(3) = 1, a(2) = 2, a(4) = a(5) = 4; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 5.

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