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%I #26 Sep 08 2022 08:44:49
%S 11,22,40,67,105,156,222,305,407,530,676,847,1045,1272,1530,1821,2147,
%T 2510,2912,3355,3841,4372,4950,5577,6255,6986,7772,8615,9517,10480,
%U 11506,12597,13755,14982,16280,17651,19097,20620,22222,23905,25671,27522,29460,31487,33605,35816,38122,40525,43027
%N a(n) = dot_product(1,2,...,n)*(3,4,...,n,1,2).
%H Vincenzo Librandi, <a href="/A026037/b026037.txt">Table of n, a(n) for n = 3..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F n(2n^2 - 3n + 13)/6. - _Ralf Stephan_, Apr 30 2004
%F G.f.: -x^3*(-11 + 22*x - 18*x^2 + 5*x^3) / (x - 1)^4 . - _R. J. Mathar_, Apr 17 2011
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 20 2012
%t s=0;lst={};Do[s+=n^2+2;If[s>10, AppendTo[lst, s]], {n, 0, 6!, 1}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 07 2008 *)
%t Table[n (2n^2-3n+13)/6,{n,3,60}] (* _Harvey P. Dale_, Apr 22 2011 *)
%t LinearRecurrence[{4,-6,4,-1},{11,22,40,67},50] (* _Vincenzo Librandi_, Jun 20 2012 *)
%o (Magma) I:=[11, 22, 40, 67]; [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 20 2012
%Y Column 2 of triangle A094414.
%K nonn,easy
%O 3,1
%A _Clark Kimberling_
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