

A100682


Floor of 4th root of pentatope numbers.


1



0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 30, 31, 31
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OFFSET

0,5


COMMENTS

Conjecture: a(n) = floor((n  3/2)/24^(1/4)) for n not in {0, 1, 6, 17, 2403, 5318}.  Charles R Greathouse IV, May 01 2012


REFERENCES

J. H. Conway and R. K. Guy, The Book of Numbers, pp. 5557, Copernicus Press, NY, 1996.


LINKS



FORMULA

a(n) = floor((A000332(n+3))^(1/4)) = floor(Ptop(n)^(1/4)) = floor(C(n+3, 4)^1/4)) = floor(((n * (n+1) * (n+2) * (n+3)/4!)^(1/4))


EXAMPLE

a(3) = 1 because floor((3*4*5*6/24)^(1/4)) = floor(15^(1/4)) = floor(1.96798967)) = 1.


MAPLE

a:= n> floor(binomial(n+3, 4)^(1/4)):


PROG

(Magma) [Floor(Binomial(n+3, 4)^(1/4)): n in [3..70]]; // Vincenzo Librandi, Dec 14 2015


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



