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A000400 Powers of 6: a(n) = 6^n.
(Formerly M4224 N1765)
106
1, 6, 36, 216, 1296, 7776, 46656, 279936, 1679616, 10077696, 60466176, 362797056, 2176782336, 13060694016, 78364164096, 470184984576, 2821109907456, 16926659444736, 101559956668416, 609359740010496, 3656158440062976, 21936950640377856, 131621703842267136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Same as Pisot sequences E(1, 6), L(1, 6), P(1, 6), T(1, 6). See A008776 for definitions of Pisot sequences.

Central terms of the triangle in A036561. - Reinhard Zumkeller, May 14 2006

a(n) = A169604(n)/3; a(n+1) = 2*A169604(n). - Reinhard Zumkeller, May 02 2010

Number of pentagons contained within pentaflakes. - William A. Tedeschi, Sep 12 2010

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 p-colored compositions of n. For n >= 1, a(n) equals the number of 5-colored 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.

~~

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

T. D. Noe, Table of n, a(n) for n=0..100

C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps, FPSAC02, Melbourne, 2002.

Peter J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 271

Tanya Khovanova, Recursive Sequences

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Yash Puri and Thomas Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Eric Weisstein's World of Mathematics, Pentaflake

Index entries for linear recurrences with constant coefficients, signature (6).

FORMULA

a(n) = 6^n.

a(0) = 1; a(n) = 6*a(n-1).

G.f.: 1/(1-6*x). - Simon Plouffe in his 1992 dissertation.

E.g.f.: exp(6*x).

A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller, Mar 04 2007

a(n) = A159991(n)/A011577(n). [Reinhard Zumkeller, May 02 2009]

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

6^Range[0, 40] (* Harvey P. Dale, Jan 24 2013 *)

PROG

(PARI) a(n)=6^n \\ Charles R Greathouse IV, Jun 16 2011

(Maxima) A000400(n):=6^n$

makelist(A000400(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */

(Haskell)

a000400 = (6 ^)

a000400_list = iterate (* 6) 1  -- Reinhard Zumkeller, Nov 21 2013

CROSSREFS

Column k = 3 of A225816.

Sequence in context: A007275 A206452 A215748 * A238936 A097681 A050736

Adjacent sequences:  A000397 A000398 A000399 * A000401 A000402 A000403

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 23 02:42 EDT 2017. Contains 288633 sequences.