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A194960 a(n) = floor((n+2)/3) + ((n-1) mod 3). 6
1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 15, 14, 15, 16, 15, 16, 17, 16, 17, 18, 17, 18, 19, 18, 19, 20, 19, 20, 21, 20, 21, 22, 21, 22, 23, 22, 23, 24, 23, 24, 25, 24, 25, 26, 25, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is formed by concatenating triples of the form (n,n+1,n+2) for n>=1.  See A194961 and A194962 for the associated fractalization and interspersion. The sequence can be obtained from A008611 by deleting its first four terms.

The sequence contains every positive integer n exactly min(n,3) times. - Wesley Ivan Hurt, Dec 17 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

a(n) = ((-1)^n*A130772(n))+n+4)/3. G.f. -x*(-1-x-x^2+2*x^3) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Sep 07 2011

a(n) = A006446(n)/floor(sqrt(A006446(n))). - Benoit Cloitre, Jan 15 2012

a(n) = a(n-1) + a(n-3) - a(n-4). - Vincenzo Librandi, Dec 17 2013

a(n) = a(n-3) + 1, n >= 1, with input a(-2) = 0, a(-1) = 1 and a(0) = 2. Proof trivial. a(n) = A008611(n+3), n >= -2. See the first comment above. - Wolfdieter Lang, May 06 2017

MAPLE

A194960:=n->floor((n+2)/3)+((n-1) mod 3); seq(A194960(n), n=1..100); # Wesley Ivan Hurt, Dec 17 2013

MATHEMATICA

p[n_] := Floor[(n + 2)/3] + Mod[n - 1, 3]

Table[p[n], {n, 1, 90}]  (* A194960 *)

g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

f[20]  (* A194961 *)

row[n_] := Position[f[30], n];

u = TableForm[Table[row[n], {n, 1, 5}]]

v[n_, k_] := Part[row[n], k];

w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},

{k, 1, n}]]  (* A194962 *)

q[n_] := Position[w, n]; Flatten[

Table[q[n], {n, 1, 80}]]  (* A194963 *)

CoefficientList[Series[(1 + x + x^2 - 2 x^3)/((1 + x + x^2) (x - 1)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Dec 17 2013 *)

PROG

(MAGMA) I:=[1, 2, 3, 2]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..100]]; // Vincenzo Librandi, Dec 17 2013

(PARI) a(n)=(n+2)\3 + (n-1)%3 \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

Cf. A008611, A194961, A194962, A194963.

Sequence in context: A100795 A045781 A045670 * A111439 A020986 A095161

Adjacent sequences:  A194957 A194958 A194959 * A194961 A194962 A194963

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 06 2011

STATUS

approved

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Last modified October 13 18:14 EDT 2019. Contains 327981 sequences. (Running on oeis4.)