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a(n) = T(10, n), array T given by A047858.
1

%I #21 Sep 08 2022 08:45:59

%S 1,12,35,83,183,391,823,1719,3575,7415,15351,31735,65527,135159,

%T 278519,573431,1179639,2424823,4980727,10223607,20971511,42991607,

%U 88080375,180355063,369098743,754974711,1543503863,3154116599,6442450935,13153337335,26843545591

%N a(n) = T(10, n), array T given by A047858.

%H Vincenzo Librandi, <a href="/A195858/b195858.txt">Table of n, a(n) for n = 0..3000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).

%F a(n) = 2^(n-1)*(n+20)-9.

%F a(0)=1, a(1)=12, a(2)=35, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3).

%F G.f.: (1+7*x-17*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Aug 24 2016

%t LinearRecurrence[{5,-8,4},{1,12,35},40] (* _Harvey P. Dale_, Jul 24 2019 *)

%o (Magma) [2^(n-1)*(n+20)-9: n in [0..30]]; // _Vincenzo Librandi_, Sep 28 2011

%o (PARI) Vec((1+7*x-17*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Aug 24 2016

%Y Cf. A047858.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Sep 28 2011