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A055272
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First differences of 7^n (A000420).
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5
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1, 6, 42, 294, 2058, 14406, 100842, 705894, 4941258, 34588806, 242121642, 1694851494, 11863960458, 83047723206, 581334062442, 4069338437094, 28485369059658, 199397583417606, 1395783083923242, 9770481587462694
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sum of A055270.
Conjecture in "Introduction a la theorie des nombres" by d'Armel Mercier and J. M. Deconinck: this is the period length of the fraction 1/7^n. For example 1/7^2=0.0204081632653061224489795918367346938775510204....with a period of 42 digits =6*7=a(2). The period of 1/7^3 has exactly 294=a(3) digits. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2002
Also phi(7^n), where phi is Euler's totient function. - Alonso Delarte (alonso.delarte(AT)gmail.com), May 08 2006
For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5,6,7} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7} we have f(x)<>y. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 27 2007
a(n) is the number of compositions of n when there are 6 types of each natural number. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
Apart from the first term, number of monic squarefree polynomials over F_7 of degree n. [Charles R Greathouse IV, Feb 07 2012]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| G.f.: (1-x)/(1-7*x).
G.f: 1/( 1 - 6*sum(k>=1, x^k) ).
a(n) = 6*7^(n-1), a(0)=1.
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MATHEMATICA
| Table[EulerPhi[7^n], {n, 0, 19}] - Alonso Delarte (alonso.delarte(AT)gmail.com), May 08 2006
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PROG
| (PARI) a(n)=round(7^n*6/7) \\ Charles R Greathouse IV, Feb 07 2012
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CROSSREFS
| Cf. A000420, A055270.
Sequence in context: A057089 A110711 A156361 * A155196 A147838 A127628
Adjacent sequences: A055269 A055270 A055271 * A055273 A055274 A055275
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Barry E. Williams, May 28 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 30 2000
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