|
%I #17 Sep 08 2022 08:45:46
%S 1,10,102,1060,11204,120200,1306008,14340560,158822416,1771073440,
%T 19856872032,223572243520,2525471411264,28599348360320,
%U 324490768902528,3687079238739200,41941489422336256,477496023050283520
%N a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
%C Binomial transform of A147960. Tenth binomial transform of A077957.
%H G. C. Greubel, <a href="/A162666/b162666.txt">Table of n, a(n) for n = 0..940</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-98).
%F a(n) = ((10+sqrt(2))^n + (10-sqrt(2))^n)/2.
%F G.f.: (1-10*x)/(1-20*x+98*x^2).
%F E.g.f.: exp(10*x)*cosh(sqrt(2)*x). - _Ilya Gutkovskiy_, Aug 11 2017
%p seq(coeff(series((1-10*x)/(1-20*x+98*x^2), x, n+1), x, n), n = 0..20); # _G. C. Greubel_, Aug 27 2019
%t Union[Flatten[NestList[{#[[2]],20#[[2]]-98#[[1]]}&,{1,10},20]]] (* _Harvey P. Dale_, Feb 25 2011 *)
%t LinearRecurrence[{20,-98}, {1,10}, 20] (* _G. C. Greubel_, Aug 27 2019 *)
%o (Magma) [ n le 2 select 9*n-8 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];
%o (PARI) my(x='x+O('x^20)); Vec((1-10*x)/(1-20*x+98*x^2)) \\ _G. C. Greubel_, Aug 27 2019
%o (Sage)
%o def A162666_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1-10*x)/(1-20*x+98*x^2)).list()
%o A162666_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]-98*a[n-2]; od; a; # _G. C. Greubel_, Aug 27 2019
%Y Cf. A147960, A077957.
%K nonn,easy
%O 0,2
%A _Klaus Brockhaus_, Jul 20 2009
| 