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%I #19 Aug 09 2017 12:43:02
%S 1,2,3,7,17,36,67,113,177,262,371,507,673,872,1107,1381,1697,2058,
%T 2467,2927,3441,4012,4643,5337,6097,6926,7827,8803,9857,10992,12211,
%U 13517,14913,16402,17987,19671,21457,23348,25347,27457,29681
%N a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).
%H G. C. Greubel, <a href="/A158498/b158498.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).
%F G.f.: x*(1 - 2*x + x^2 + 3*x^3) / (1-x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _G. C. Greubel_, Feb 19 2017
%t Table[(1/2)*(n^3 - 6*n^2 + 13*n - 6), {n,1,50}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1,2,3,7}, 50] (* _G. C. Greubel_, Feb 19 2017 *)
%o (PARI) x='x+O('x^50); Vec(x*(1 - 2*x + x^2 + 3*x^3) / (1-x)^4) \\ _G. C. Greubel_, Feb 19 2017
%o (PARI) a(n)=(n^3 - 6*n^2 + 13*n - 6)/2 \\ _Charles R Greathouse IV_, Feb 19 2017
%K nonn,easy
%O 1,2
%A _Alexander R. Povolotsky_, Jan 13 2011
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