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a(n) = T(6,n), array T given by A047858.
1

%I #23 Sep 08 2022 08:44:57

%S 1,8,23,55,123,267,571,1211,2555,5371,11259,23547,49147,102395,212987,

%T 442363,917499,1900539,3932155,8126459,16777211,34603003,71303163,

%U 146800635,301989883,620756987,1275068411,2617245691

%N a(n) = T(6,n), array T given by A047858.

%H Vincenzo Librandi, <a href="/A048467/b048467.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 G.f.: (-9*x^2 + 3*x + 1)/((1-x)*(1-2*x)^2).

%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - _Harvey P. Dale_, Jul 07 2011

%F a(n) = 2^(n-1)*(n+12) - 5. - _Vincenzo Librandi_, Sep 28 2011

%t LinearRecurrence[{5,-8,4},{1,8,23},30] (* or *) CoefficientList[ Series[ (-9x^2+3x+1)/((1-x)(1-2x)^2),{x,0,30}],x] (* _Harvey P. Dale_, Jul 07 2011 *)

%o (Magma) [2^(n-1)*(n+12)-5: n in [0..30]]; // _Vincenzo Librandi_, Sep 28 2011

%o (PARI) Vec((-9*x^2+3*x+1)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Andrew Howroyd_, Feb 15 2018

%Y n-th difference of a(n), a(n-1), ..., a(0) is (7, 8, 9, ...).

%K nonn,easy

%O 0,2

%A _Clark Kimberling_