%I #27 Mar 29 2023 03:40:13

%S 6,17,34,58,90,131,182,244,318,405,506,622,754,903,1070,1256,1462,

%T 1689,1938,2210,2506,2827,3174,3548,3950,4381,4842,5334,5858,6415,

%U 7006,7632,8294,8993,9730,10506,11322,12179,13078,14020,15006,16037,17114,18238,19410,20631

%N Convolution of natural numbers >= 2 and natural numbers >= 3.

%H Vincenzo Librandi, <a href="/A023545/b023545.txt">Table of n, a(n) for n = 1..1000</a>

%H László Németh, <a href="https://arxiv.org/abs/1905.13475">Tetrahedron trinomial coefficient transform</a>, arXiv:1905.13475 [math.CO], 2019.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = n*(n^2 + 12*n + 23)/6. - _Ralf Stephan_, Feb 15 2004; corrected by Lucas Sidiropoulos (lsid77(AT)yahoo.com), Jun 23 2008

%F From _Colin Barker_, Jun 20 2012: (Start)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F G.f.: x*(2 - x)*(3 - 2*x)/(1 - x)^4. (End)

%F E.g.f.: exp(x)*x*(36 + 15*x + x^2)/6. - _Stefano Spezia_, Mar 28 2023

%t CoefficientList[Series[(2-x)*(3-2*x)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 29 2012 *)

%t LinearRecurrence[{4,-6,4,-1},{6,17,34,58},50] (* _Harvey P. Dale_, Aug 10 2014 *)

%o (Magma) I:=[6, 17, 34, 58]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 29 2012

%K nonn,easy

%O 1,1

%A _Clark Kimberling_