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A000351
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Powers of 5.
(Formerly M3937 N1620)
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94
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1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125, 244140625, 1220703125, 6103515625, 30517578125, 152587890625, 762939453125, 3814697265625, 19073486328125, 95367431640625, 476837158203125, 2384185791015625, 11920928955078125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Same as Pisot sequences E(1,5), L(1,5), P(1,5), T(1,5). See A008776 for definitions of Pisot sequences.
a(n) has leading digit 1 iff n = A067497 - 1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 09 2002
With interpolated zeros 0,1,0,5,0,25,... (G.f.: x/(1-5x^2)) second inverse binomial transform of Fib(3n)/F(3) (A001076). Binomial transform is A085449. - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004
Sums of rows of the triangles in A013620 and A038220. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2006
Contribution by Adi Dani, Jun 22 2011: (Start)
Sum of coefficients of expansion of (1+x+x^2+x^3+x^4)^n.
a(n) is number of compositions of natural numbers into n parts <5.
a(2)=25 there are 25 compositions of natural numbers into 2 parts <5. (End)
The compositions of n in which each natural number 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.
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 270
Tanya Khovanova, Recursive Sequences
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Eric Weisstein's World of Mathematics, Box Fractal
Index entries for sequences related to linear recurrences with constant coefficients, signature (5).
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FORMULA
| a(n) = 5^n.
a(n) = 5*a(n-1).
G.f.: 1/(1-5*x).
E.g.f.: exp(5*x).
a(n) = A006495(n)^2 + A006496(n)^2.
a(n) = A159991(n)/A001021(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2009]
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MAPLE
| [ seq(5^n, n=0..30) ];
A000351:=-1/(-1+5*z); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[5^n, {n, 0, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006
5^Range[0, 30] (* From Harvey P. Dale, Aug 22 2011 *)
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PROG
| (PARI) a(n)=5^n \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
| a(n) = A006495(n)^2 + A006496(n)^2.
a(n) = A159991(n)/A001021(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2009]
Sequence in context: A129066 A102169 A060391 * A050735 A195948 A083590
Adjacent sequences: A000348 A000349 A000350 * A000352 A000353 A000354
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Removed attribute "conjectured" from Plouffe g.f R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 11 2009
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