A094294 -id:A094294 - cp's OEIS frontend

A019502 Number of simplices in minimal decomposition of an n-cube.

1, 2, 5, 16, 67

Offset: 1

H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, Section C9.
R. K. Guy, What is the simplexity of the d-cube?, Amer. Math. Monthly, 91:10 (1984), 628-629.

A. Bliss, F. E. Su, Lower bounds for simplicial covers and triangulations of cubes, arXiv:math/0310142 [math.CO], 2003 (see Table 1 page 4).
A. Bliss, F. E. Su. Lower bounds for simplicial covers and triangulations of cubes, Discrete Comput. Geom. 33 (2005), 669-686.
R. B. Hughes and M. R. Anderson, Simplexity of the cube, Discrete Math., 158(1-3):99-150, 1996.
John F. Sallee, A note on minimal triangulations of an n-cube, Discrete Appl. Math. 4 (1982), no. 3, 211--215. MR0675850 (84g:52019).
John F. Sallee, The middle-cut triangulations of the n-cube, SIAM J. Algebraic Discrete Methods 5 (1984), no. 3, 407--419. MR0752044 (86c:05054). See Table 2.
John F. Sallee, A triangulation of the n-cube, Discrete Math. 40 (1982), no. 1, 81--86. MR0676714 (84d:05065b).

Other sequences dealing with different ways to attack this problem. They give further references: A019503, A019504, A166932, A166932, A239912, A275518.

A094293 At the n-th step, append the number n and n copies of the list of all preceding terms, starting with an empty list.

Original entry on oeis.org

1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 4, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 5, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 4

Offset: 1

Amarnath Murthy, Apr 28 2004

nonn

a(1)= 1, a(2) = 2. Let the index of first occurrence of n be k=A094294(n). Then from a(k+1) onwards the next n*(k-1) terms are the first (k-1) terms repeated n times, a(k+1) = a(1), a(k+2) = a(2) etc.

Let r be the index of the first occurrence of n-1 then the index of first occurrence of n is r+(n-1)*(r-1)+1 = (n+1)*r-n+2, cf. A094294. [Corrected by M. F. Hasler, Apr 09 2009]

			a(5) = 3 and the first four terms are 1,2,1,1. hence the next 12 terms are 1,2,1,1,1,2,1,1,1,2,1,1 and a(18) = 4 (the first occurrence) and so on.
(Contribution by _M. F. Hasler_, start:) The sequence is created as follows:
First step: append 1 to the empty list: result = [1].
2nd step: append 2 and two copies of the previous result, to get [1,2,1,1].
3rd step: append 3 and three copies of [1,2,1,1], to get [1,2,1,1, 3, 1,2,1,1, 1,2,1,1, 1,2,1,1].

Cf. A001511.

A094293(n,a=[])={ for(k=1,1+n--, n<=(k+1)*#a & return(if(n>#a,a[1+(n-1)%#a],k)); a=concat(vector(k+2,j,if(j==2,[k],a))))} \\ M. F. Hasler, Apr 09 2009

Edited & corrected by M. F. Hasler, Apr 10 2009

A130193 a(0)=1. a(n+1) = a(ceiling(n/a(n))) + 1.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6, 5, 6, 5, 5

Offset: 0

Leroy Quet, Aug 05 2007

Records 1,2,3,4,5,... appear at n = 0, 1, 2, 5, 18, 87, 518, 3621,.. which appears to be essentially A094294. - R. J. Mathar, Sep 10 2015

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

Cf. A094294, A130147.

A130193 := proc(n)
    option remember;
    if n = 0 then
        1;
    else
        1+procname(ceil((n-1)/procname(n-1))) ;
    end if;
end proc:
seq(A130193(n),n=0..50) ; # R. J. Mathar, Sep 10 2015

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A019502 Number of simplices in minimal decomposition of an n-cube.

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A094293 At the n-th step, append the number n and n copies of the list of all preceding terms, starting with an empty list.

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A130193 a(0)=1. a(n+1) = a(ceiling(n/a(n))) + 1.

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