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%I #29 Nov 15 2023 19:08:49
%S 0,1,13,127,1105,9031,70993,543607,4085185,30275911,222009073,
%T 1614529687,11664504865,83828316391,599858908753,4277376525367,
%U 30411820662145,215703854542471,1526853641242033,10789535445362647
%N a(n) = 7^n - 6^n.
%C a(n) is also the number of n-digit numbers whose smallest decimal digit is 3. - _Stefano Spezia_, Nov 15 2023
%H John Elias, <a href="/A016169/a016169.png">Illustration of initial terms: a star number fractal</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-42).
%F G.f.: x/((1-6x)(1-7x)).
%F E.g.f.: e^(7*x) - e^(6*x). [_Mohammad K. Azarian_, Jan 14 2009]
%F a(0)=0, a(n) = 7*a(n-1) + 6^(n-1). [_Vincenzo Librandi_, Feb 09 2011]
%F a(0)=0, a(1)=1, a(n) = 13*a(n-1) - 42*a(n-2). [_Vincenzo Librandi_, Feb 09 2011]
%p a:=n->sum(6^(n-j)*binomial(n,j),j=1..n): seq(a(n), n=0..19); # _Zerinvary Lajos_, Apr 18 2009
%t Table[7^n-6^n,{n,0,20}] (* or *) LinearRecurrence[{13,-42},{0,1},20] (* _Harvey P. Dale_, Apr 25 2020 *)
%Y Cf. A016177, A016189.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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