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%I #20 Dec 21 2024 23:51:11
%S 1,2,10,30,78,190,446,1022,2302,5118,11262,24574,53246,114686,245758,
%T 524286,1114110,2359294,4980734,10485758,22020094,46137342,96468990,
%U 201326590,419430398,872415230,1811939326,3758096382,7784628222,16106127358,33285996542,68719476734
%N a(3) = 1, otherwise a(n) = n*2^(n-3) - 2^(n-2) - 2.
%D B. Elspas, The theory of multirail cascades, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Ac. Press, 1971, Chap. 8, see esp. p. 361 (S_1(n)).
%H Harry J. Smith, <a href="/A058966/b058966.txt">Table of n, a(n) for n = 3...200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F From _Colin Barker_, Mar 23 2012: (Start)
%F a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3) for n>6.
%F G.f.: x^3*(1-3*x+8*x^2-8*x^3)/((1-x)*(1-2*x)^2). (End)
%t Join[{1},Table[n*2^(n-3)-2^(n-2)-2,{n,4,40}]] (* or *) LinearRecurrence[ {5,-8,4},{1,2,10,30},40] (* _Harvey P. Dale_, Dec 22 2019 *)
%o (PARI) a(n) = { abs(n*2^(n-3)-2^(n-2)-2) } \\ _Harry J. Smith_, Jun 24 2009
%K nonn,easy
%O 3,2
%A _N. J. A. Sloane_, Jan 14 2001