A275518 Number of simplices in corner-cut triangulation of the n-cube.
1, 2, 5, 16, 67, 364, 2445, 19296, 173015, 1728604, 19011049, 228124384, 2965598547, 41518338684, 622774990133, 9964399645504, 169394793547567, 3049106282938684, 57933019373868897, 1158660387473183616, 24331868136927943019, 535301099012395872028
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Carl W. Lee, Triangulating the d-cube, Annals of the New York Academy of Sciences 440 (1985): 205-211.
- 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)
Programs
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Maple
p := proc(d,x) add( x^i/i!,i=0..d) ; end proc: A275518 := proc(d) d!*(p(d,2)/2-p(d,1))+2^(d-1)-d!/2+1 ; end proc: seq(A275518(d),d=1..18) ; -
Mathematica
p[d_, x_] := Sum[x^i/i!, {i, 0, d}]; A275518[d_] := d!*(p[d, 2]/2 - p[d, 1]) + 2^(d - 1) - d!/2 + 1; Table[A275518[d], {d, 1, 18}] (* Jean-François Alcover, Sep 06 2023, after Maple program *) -
PARI
a(n) = 1 + 2^(n-1) - n! + n!*sum(i=1, n, (2^(i-1)-1)/i!) \\ Andrew Howroyd, Sep 06 2023
Formula
a(n) = 1 + 2^(n-1) - n! + n!*Sum_{i=1..n} (2^(i-1)-1)/i!. - Andrew Howroyd, Sep 06 2023, after Maple program
Extensions
Terms a(19) and beyond from Andrew Howroyd, Sep 06 2023
Comments