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 A048478 a(n) = T(6,n), array T given by A048472. 1

%I

%S 1,8,29,85,225,561,1345,3137,7169,16129,35841,78849,172033,372737,

%T 802817,1720321,3670017,7798785,16515073,34865153,73400321,154140673,

%U 322961409,675282945,1409286145,2936012801,6106906625,12683575297,26306674689,54492397569

%N a(n) = T(6,n), array T given by A048472.

%C n-th difference of a(n), a(n-1), ..., a(0) is (7, 14, 21, ...).

%H Vincenzo Librandi, <a href="/A048478/b048478.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = 7*n * 2^(n-1) + 1.

%F a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3) for n>2. G.f.: (1+3*x-3*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Feb 18 2016

%o (MAGMA) [7*n * 2^(n-1) + 1: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011

%o (PARI) Vec((1+3*x-3*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 18 2016

%K nonn,easy

%O 0,2

%A _Clark Kimberling_

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