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A104896
a(0) = 0; a(n) = 7*a(n-1) + 7.
3
0, 7, 56, 399, 2800, 19607, 137256, 960799, 6725600, 47079207, 329554456, 2306881199, 16148168400, 113037178807, 791260251656, 5538821761599, 38771752331200, 271402266318407, 1899815864228856, 13298711049601999, 93090977347214000, 651636841430498007
OFFSET
0,2
COMMENTS
Conjecture: this is also the number of integers from 0 to 10^n - 1 that lack 0, 1 and 2 as a digit.
Number of monic irreducible polynomials of degree 1 in GF(7)[x1,...,xn]. - Max Alekseyev, Jan 23 2006
FORMULA
a(n) = (7^(n+1) - 7) / 6. - Max Alekseyev, Jan 23 2006
a(n) = a(n-1) + 7^n with a(0)=0. - Vincenzo Librandi, Nov 13 2010
From Colin Barker, Jul 25 2014: (Start)
a(n) = 8*a(n-1) - 7*a(n-2).
G.f.: 7*x / ((x-1)*(7*x-1)). (End)
E.g.f.: (7/6)*(exp(7*x) - exp(x)). - G. C. Greubel, Jun 09 2021
MAPLE
a:=n->sum (7^j, j=1..n): seq(a(n), n=0..30); # Zerinvary Lajos, Oct 03 2007
MATHEMATICA
RecurrenceTable[{a[n]==7*a[n-1]+7, a[0]==0}, a, {n, 0, 30}] (* Vaclav Kotesovec, Jul 25 2014 *)
PROG
(PARI) concat(0, Vec(7*x/((x-1)*(7*x-1)) + O(x^30))) \\ Colin Barker, Jul 25 2014
(Magma) [(7/6)*(7^n -1): n in [0..30]]; // G. C. Greubel, Jun 09 2021
(Sage) [(7/6)*(7^n -1) for n in (0..30)] # G. C. Greubel, Jun 09 2021
CROSSREFS
Row n=7 of A228275.
Sequence in context: A054614 A270240 A344066 * A246939 A122996 A343364
KEYWORD
easy,nonn
AUTHOR
Alexandre Wajnberg, Apr 24 2005
STATUS
approved