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A055272
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First differences of 7^n (A000420).
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9
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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;
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history;
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OFFSET
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0,2
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COMMENTS
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Conjecture in "Introduction à la théorie des nombres" by J. M. Deconinck and Armel Mercier: 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, Feb 02 2002
Also phi(7^n), where phi is Euler's totient function. - Alonso del Arte, 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 Janjic, Mar 27 2007
a(n) is the number of compositions of n when there are 6 types of each part. - Milan Janjic, 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
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Jean-Marie De Koninck and Armel Mercier, Introduction à la théorie des nombres, Collection Universitaire de Mathématiques, Modulo, 1994.
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LINKS
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FORMULA
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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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MAPLE
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MATHEMATICA
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PROG
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(Sage) [1]+[6*7^(n-1) for n in (1..20)] # G. C. Greubel, Mar 16 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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