A011577 -id:A011577 - cp's OEIS frontend

A000400 Powers of 6: a(n) = 6^n.

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

Offset: 0

N. J. A. Sloane

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.
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. - 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
a(n) is the number of possible outcomes of n distinguishable 6-sided dice. - Stefano Spezia, Jul 06 2024

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 86.
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).

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; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 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).

Column 3 of A225816.
Row 6 of A003992.
Row 3 of A329332.
Cf. A000005, A000290, A011577, A036561, A159991, A169604,

a000400 = (6 ^)
a000400_list = iterate (* 6) 1  -- Reinhard Zumkeller, Nov 21 2013

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

A000400(n):=6^n$
makelist(A000400(n),n,0,30); /* Martin Ettl, Nov 05 2012 */

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

(List.fill(50)(6: BigInt)).scanLeft(1: BigInt)( * ) // Alonso del Arte, May 31 2019

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

A137233 Number of n-digit even numbers.

Original entry on oeis.org

5, 45, 450, 4500, 45000, 450000, 4500000, 45000000, 450000000, 4500000000, 45000000000, 450000000000, 4500000000000, 45000000000000, 450000000000000, 4500000000000000, 45000000000000000, 450000000000000000, 4500000000000000000, 45000000000000000000, 450000000000000000000

Offset: 1

Ctibor O. Zizka, Mar 08 2008

From Kival Ngaokrajang, Oct 18 2013: (Start)
a(n) is also the total number of double rows identified numbers in n digit.
For example:
  n = 1: 01 23 45 67 89 = 5 double rows;
  n = 2: 1011 1213 1415 1617 1819...9899 = 45 double rows;
  n = 3: 100101 102103 104105...998999 = 450 double rows;
The number of double rows is also A030656. (End)
a(n) is also the number of n-digit integers with an even number of even digits (A356929); a(5) = 45000 is the answer to the question 2 of the Olympiade Mathématique Belge in 2004 (link). - Bernard Schott, Sep 06 2022
a(n) is also the number of n-digit integers with an odd number of odd digits (A054684). - Bernard Schott, Nov 07 2022

			a(2) = 45 because there are 45 2-digit even numbers.

Olympiade Mathématique Belge, OMB 2004, Finale Maxi, Question 2.
Index to sequences related to Olympiads.
Index entries for linear recurrences with constant coefficients, signature (10).

Cf. A000422, A002275, A002276, A011577, A014923, A014925, A016313, A019518, A037487, A053052, A057138, A090843, A097166, A099914, A099915.

Cf. A030656, A052268, A054684, A356929.

Vec(5*x*(1-x)/(1-10*x) + O(x^22)) \\ Elmo R. Oliveira, Jul 23 2025

def A137233(n): return 9*10**(n-1)+1>>1 # Chai Wah Wu, Nov 11 2022

a(n) = 9*10^(n-1)/2 if n > 1. - R. J. Mathar, May 23 2008
From Elmo R. Oliveira, Jul 23 2025: (Start)
G.f.: 5*x*(1-x)/(1-10*x).
E.g.f.: (-9 + 10*x + 9*exp(10*x))/20.
a(n) = 10*a(n-1) for n > 2.
a(n) = A052268(n)/2 for n >= 2. (End)

Corrected and extended by R. J. Mathar, May 23 2008

More terms from Elmo R. Oliveira, Jul 23 2025

cp's OEIS Frontend

A000400 Powers of 6: a(n) = 6^n.

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