%I #17 Apr 03 2023 18:02:35
%S 1,4,15,42,93,176,299,470,697,988,1351,1794,2325,2952,3683,4526,5489,
%T 6580,7807,9178,10701,12384,14235,16262,18473,20876,23479,26290,29317,
%U 32568,36051,39774,43745,47972,52463,57226,62269,67600,73227,79158
%N Bisection of A000125.
%H G. C. Greubel, <a href="/A100503/b100503.txt">Table of n, a(n) for n = 0..5000</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) = (4*n^3 + 5*n + 3)/3. - _Ralf Stephan_, May 15 2007
%F From _Colin Barker_, Aug 20 2012: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: (1+5*x^2+2*x^3)/(1-x)^4. (End)
%F E.g.f.: (3 + 9*x + 12*x^2 + 4*x^3)*exp(x). - _G. C. Greubel_, Apr 03 2023
%t LinearRecurrence[{4,-6,4,-1},{1,4,15,42},40] (* _Harvey P. Dale_, Apr 12 2013 *)
%o (Magma) [(4*n^3+5*n+3)/3: n in [0..40]]; // _G. C. Greubel_, Apr 03 2023
%o (SageMath) [1+n*(4*n^2+5)/3 for n in range(41)] # _G. C. Greubel_, Apr 03 2023
%Y Cf. A000125.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 24 2004
%E More terms from _Hugo Pfoertner_, Nov 25 2004