

A000400


Powers of 6: a(n) = 6^n.
(Formerly M4224 N1765)


169



1, 6, 36, 216, 1296, 7776, 46656, 279936, 1679616, 10077696, 60466176, 362797056, 2176782336, 13060694016, 78364164096, 470184984576, 2821109907456, 16926659444736, 101559956668416, 609359740010496, 3656158440062976, 21936950640377856, 131621703842267136
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OFFSET

0,2


COMMENTS

Same as Pisot sequences E(1, 6), L(1, 6), P(1, 6), T(1, 6). Essentially same as Pisot sequences E(6, 36), L(6, 36), P(6, 36), T(6, 36). See A008776 for definitions of Pisot sequences.
Sum of coefficients of expansion of (1 + x + x^2 + x^3 + x^4 + x^5)^n.
a(n) is number of compositions of natural numbers into n parts less than 6. For example, a(2) = 36, and there are 36 compositions of natural numbers into 2 parts less than 6.
The compositions of n in which each part is colored by one of p different colors are called pcolored compositions of n. For n >= 1, a(n) equals the number of 5colored compositions of n such that no adjacent parts have the same color.
Number of words of length n over the alphabet of six letters.  Joerg Arndt, Sep 16 2014
The number of ordered triples (x, y, z) of binary words of length n such that D(x,z) = D(x, y) + D(y, z) where D(a, b) is the Hamming distance from a to b.  Geoffrey Critzer, Mar 06 2017
a(n) is the area of a triangle with vertices at (2^n, 3^n), (2^(n+1), 3^(n+1)), and (2^(n+2), 3^(n+2)); a(n) is also one fifth the area of a triangle with vertices at (2^n, 3^(n+2)), (2^(n+1), 3^(n+1)), and (2^(n+2), 3^n).  J. M. Bergot, May 07 2018


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA

a(n) = 6^n.
a(0) = 1; a(n) = 6*a(n1).
E.g.f.: exp(6*x).
a(n) = det(s(i+3,j), 1 <= i,j <= n), where s(n,k) are Stirling numbers of the first kind.  Mircea Merca, Apr 04 2013


MATHEMATICA



PROG

(Haskell)
a000400 = (6 ^)
(Scala) (List.fill(50)(6: BigInt)).scanLeft(1: BigInt)(_ * _) // Alonso del Arte, May 31 2019


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



