

A055272


First differences of 7^n (A000420).


5



1, 6, 42, 294, 2058, 14406, 100842, 705894, 4941258, 34588806, 242121642, 1694851494, 11863960458, 83047723206, 581334062442, 4069338437094, 28485369059658, 199397583417606, 1395783083923242, 9770481587462694
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OFFSET

0,2


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, 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 natural number.  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


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194196.


LINKS

Table of n, a(n) for n=0..19.
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (7).


FORMULA

G.f.: (1x)/(17*x).
G.f: 1/( 1  6*sum(k>=1, x^k) ).
a(n) = 6*7^(n1), a(0)=1.


MATHEMATICA

Table[EulerPhi[7^n], {n, 0, 19}] (* Alonso del Arte, May 08 2006 *)


PROG

(PARI) a(n)=round(7^n*6/7) \\ Charles R Greathouse IV, Feb 07 2012


CROSSREFS

Cf. A000420, A055270.
Sequence in context: A110711 A156361 A216517 * A155196 A147838 A127628
Adjacent sequences: A055269 A055270 A055271 * A055273 A055274 A055275


KEYWORD

easy,nonn


AUTHOR

Barry E. Williams, May 28 2000


STATUS

approved



