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A162667 a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 1, a(1) = 10. 1

%I

%S 1,10,103,1090,11809,130450,1463527,16616890,190375681,2195675290,

%T 25447064743,295960791730,3450850554529,40308814292770,

%U 471443782066087,5518920654923050,64648366238050561,757632021233475370

%N a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

%C Binomial transform of A152056. Tenth binomial transform of powers of 3 interleaved with zeros.

%H G. C. Greubel, <a href="/A162667/b162667.txt">Table of n, a(n) for n = 0..930</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-97).

%F a(n) = ((10+sqrt(3))^n + (10-sqrt(3))^n)/2.

%F G.f.: (1-10*x)/(1-20*x+97*x^2).

%p seq(coeff(series((1-10*x)/(1-20*x+97*x^2), x, n+1), x, n), n = 0..20); # _G. C. Greubel_, Aug 27 2019

%t LinearRecurrence[{20,-97}, {1,10}, 20] (* _G. C. Greubel_, Aug 27 2019 *)

%o (MAGMA) [ n le 2 select 9*n-8 else 20*Self(n-1)-97*Self(n-2): n in [1..18] ];

%o (PARI) my(x='x+O('x^20)); Vec((1-10*x)/(1-20*x+97*x^2)) \\ _G. C. Greubel_, Aug 27 2019

%o (Sage)

%o def A162667_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P((1-10*x)/(1-20*x+97*x^2)).list()

%o A162667_list(20) # _G. C. Greubel_, Aug 27 2019

%o (GAP) a:=[1,10];; for n in [3..20] do a[n]:=20*a[n-1]-97*a[n-2]; od; a; # _G. C. Greubel_, Aug 27 2019

%Y Cf. A152056, A000244 (powers of 3).

%K nonn,easy

%O 0,2

%A _Klaus Brockhaus_, Jul 15 2009

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Last modified May 9 04:06 EDT 2021. Contains 343685 sequences. (Running on oeis4.)