A194272 Array T(n,k) with 6 columns read by rows in which row n lists 3*n-2, 3*n-1, 3*n, 3*n, 3*n, 3*n.

1, 2, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 27, 27, 27, 27, 28, 29, 30, 30, 30, 30, 31, 32, 33, 33, 33, 33, 34, 35, 36, 36, 36, 36

Offset

1,2

Comments

Also first differences of A194273 which is also a sequence related to cellular automata.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1).

Formula

From Michael Somos, May 12 2014: (Start)

Euler transform of length 6 sequence [2, 0, -1, 0, 0, 1].

G.f.: x * (1-x^3) / ( (1-x)^2 * (1-x^6) ).

a(n-1) = A047926(n) - A132868(n). (End)

From Wesley Ivan Hurt, Apr 04 2015, Sep 08 2015: (Start)

a(n) = 2*a(n-1)-a(n-2)-a(n-3)+2*a(n-4)-a(n-5), n>5.

a(n) = floor((n+3)/6) + floor((n+4)/6) + floor((n+5)/6).

a(n) = Sum_{i=0..n-1} floor(i/6) - floor((i-3)/6). (End)

Example

Array begins:
1,  2,  3,  3,  3,  3,
4,  5,  6,  6,  6,  6,
7,  8,  9,  9,  9,  9,
10, 11, 12, 12, 12, 12,
13, 14, 15, 15, 15, 15,
16, 17, 18, 18, 18, 18,
19, 20, 21, 21, 21, 21,
22, 23, 24, 24, 24, 24,
...
Sum of row n gives 18*n-3 = A008600(n) - 3.
G.f. = x + 2*x^2 + 3*x^3 + 3*x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + ...

Maple

A194272:=n->floor((n+3)/6) + floor((n+4)/6) + floor((n+5)/6): seq(A194272(n), n=1..100); # Wesley Ivan Hurt, Apr 04 2015

Mathematica

Table[Floor[(n + 3)/6] + Floor[(n + 4)/6] + Floor[(n + 5)/6], {n, 100}] (* Wesley Ivan Hurt, Apr 04 2015 *)

Prog

(Magma) [Floor((n+3)/6) + Floor((n+4)/6) + Floor((n+5)/6) : n in [1..100]]; // Wesley Ivan Hurt, Apr 04 2015
(PARI) x='x+O('x^60); Vec(x*(1-x^3)/((1-x)^2*(1-x^6))) \\ G. C. Greubel, Aug 13 2018

Crossrefs

Column 1: A016777. Column 2: A016789. Every column 3, 4, 5 and 6: positive integers of A008585.

Cf. A008600, A047926, A132868, A194273.

Sequence in context: A064952 A255070 A176001 * A285764 A025776 A120505

Adjacent sequences: A194269 A194270 A194271 * A194273 A194274 A194275

Keyword

nonn,easy,tabf

Author

Omar E. Pol, Aug 20 2011

Status

approved