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%I #42 Nov 14 2024 10:07:41
%S 2,7,18,35,58,87,122,163,210,263,322,387,458,535,618,707,802,903,1010,
%T 1123,1242,1367,1498,1635,1778,1927,2082,2243,2410,2583,2762,2947,
%U 3138,3335,3538,3747,3962,4183,4410,4643,4882,5127,5378,5635,5898,6167,6442
%N a(n) = 3*n^2 - 4*n + 3.
%C First bisection of A133146.
%C Also first bisection of A271713. - _Bruno Berselli_, Mar 19 2021
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A133146(2*n-2) = (n - 2)^2 + (n - 1)*(n + 1) + n^2.
%F First differences: a(n+1) - a(n) = A016969(n-1).
%F G.f.: x*(2 + x + 3*x^2)/(1 - x)^3. - _R. J. Mathar_, Oct 15 2008
%F a(n) = 6*n + a(n-1) - 7 for n > 1, a(1)=2. - _Vincenzo Librandi_, Nov 25 2010
%F a(n) = 2*A000290(n)^2 + A067998(n-1) = 2*n^2 + (n - 1)*(n - 3). - _L. Edson Jeffery_, Nov 30 2013
%F From _Elmo R. Oliveira_, Nov 13 2024: (Start)
%F E.g.f.: exp(x)*(3*x^2 - x + 3) - 3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t Table[3 n^2 - 4 n + 3, {n, 50}] (* _Harvey P. Dale_, Oct 28 2012 *)
%o (PARI) a(n)=3*n^2-4*n+3 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000004 (third differences), A010722 (second differences).
%Y Cf. A000290, A016969, A067998, A133146, A271713.
%K nonn,less,easy
%O 1,1
%A _Paul Curtz_, Aug 28 2008
%E Edited and extended by _R. J. Mathar_, Oct 15 2008