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 A034857 C(n+2,3)+2*C(n,2)+2*(n-2). 1

%I

%S -1,6,18,36,61,94,136,188,251,326,414,516,633,766,916,1084,1271,1478,

%T 1706,1956,2229,2526,2848,3196,3571,3974,4406,4868,5361,5886,6444,

%U 7036,7663,8326,9026,9764,10541,11358

%N C(n+2,3)+2*C(n,2)+2*(n-2).

%D J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

%H Vincenzo Librandi, <a href="/A034857/b034857.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F (n^3 + 9n^2 + 8n - 24)/6. - Ralf Stephan, Feb 15 2004

%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: x*(-1 +10*x -12*x^2 +4*x^3)/(1- x)^4. - _Colin Barker_, Sep 09 2012

%t Table[(n^3 + 9n^2 + 8n - 24)/6,{n, 1, 60}] ( * _Vincenzo Librandi_, Sep 09 2012 *)

%o (MAGMA) [(n^3 + 9*n^2 + 8*n - 24)/6: n in [1..40]] // _Vincenzo Librandi_, Sep 09 2012

%K sign,easy

%O 1,2

%A _N. J. A. Sloane_.

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