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%I #27 Jun 13 2015 00:55:22
%S 6,10,20,46,116,310,860,2446,7076,20710,61100,181246,539636,1610710,
%T 4815740,14414446,43177796,129402310,387944780,1163310046,3488881556,
%U 10464547510,31389448220,94159956046,282463090916,847355718310
%N a(n) = 2^(n+1) + 3^n + 3.
%C This is the sequence of third terms of "second partial sums of m-th powers".
%H Colin Barker, <a href="/A254028/b254028.txt">Table of n, a(n) for n = 0..1000</a>
%H Luciano Ancora, <a href="/A254028/a254028_2.pdf">Demonstration of formulas</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F G.f.: -2*(13*x^2-13*x+3) / ((x-1)*(2*x-1)*(3*x-1)). - _Colin Barker_, Jan 24 2015
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3). - _Colin Barker_, Jan 24 2015
%F a(n) = A085279(n+1) = 2*( A099754(n)+1 ) = 2*( A094374(n)-2 ). [_Bruno Berselli_, Jan 26 2015]
%o (PARI) a(n)=2<<n + 3^n + 3 \\ _Charles R Greathouse IV_, Jan 23 2015
%o (PARI) Vec(-2*(13*x^2-13*x+3)/((x-1)*(2*x-1)*(3*x-1)) + O(x^100)) \\ _Colin Barker_, Jan 24 2015
%Y Cf. A085279, A094374, A099754.
%K nonn,easy
%O 0,1
%A _Luciano Ancora_, Jan 22 2015
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