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A037719 Base-7 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,1,3. 2

%I #16 Nov 04 2019 19:55:47

%S 2,14,99,696,4874,34118,238827,1671792,11702546,81917822,573424755,

%T 4013973288,28097813018,196684691126,1376792837883,9637549865184,

%U 67462849056290,472239943394030,3305679603758211,23139757226307480,161978300584152362,1133848104089066534

%N Base-7 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,1,3.

%H Colin Barker, <a href="/A037719/b037719.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,8,-7).

%F a(n) = 8*a(n-1) - 8*a(n-2) + 8*a(n-3) - 7*a(n-4).

%F From _Colin Barker_, Dec 24 2015: (Start)

%F a(n) = 1/100*(-(2-11*i)*(-i)^n-(2+11*i)*i^n+29*7^n-25) where i=sqrt(-1).

%F G.f.: x*(2-2*x+3*x^2) / ((1-x)*(1-7*x)*(1+x^2)).

%F (End)

%t Table[FromDigits[PadRight[{},n,{2,0,1,3}],7],{n,30}] (* or *) LinearRecurrence[ {8,-8,8,-7},{2,14,99,696},30] (* _Harvey P. Dale_, Nov 04 2019 *)

%o (PARI) Vec(x*(2-2*x+3*x^2)/((1-x)*(1-7*x)*(1+x^2)) + O(x^30)) \\ _Colin Barker_, Dec 24 2015

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)