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A000420
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Powers of 7.
(Formerly M4431 N1874)
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43
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1, 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, 40353607, 282475249, 1977326743, 13841287201, 96889010407, 678223072849, 4747561509943, 33232930569601, 232630513987207, 1628413597910449, 11398895185373143, 79792266297612001, 558545864083284007
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Same as Pisot sequences E(1,7), L(1,7), P(1,7), T(1,7). See A008776 for definitions of Pisot sequences.
Sum of coefficients of expansion of (1+x+x^2+x^3+x^4+x^5+x^6)^n
a(n) is number of compositions of natural numbers into n parts <7
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 7-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
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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 272
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.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 7^n; a(n) = 7*a(n-1).
G.f.: 1/(1-7*x).
E.g.f.: exp(7*x).
4/7 -5/7^2 +4/7^3 -5/7^4+... = 23/48. [Jolley, Summation of Series, Dover, 1961]
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EXAMPLE
| a(2)=49 there are 49 compositions of natural numbers into 2 parts <7.
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MAPLE
| A000420:=-1/(-1+7*z); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[7^n, {n, 0, 50}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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CROSSREFS
| Sequence in context: A045578 A126627 A206453 * A050737 A195908 A033143
Adjacent sequences: A000417 A000418 A000419 * A000421 A000422 A000423
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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