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%I #22 Aug 05 2024 08:44:02
%S 0,1,9,38,102,215,391,644,988,1437,2005,2706,3554,4563,5747,7120,8696,
%T 10489,12513,14782,17310,20111,23199,26588,30292,34325,38701,43434,
%U 48538,54027,59915,66216,72944,80113,87737,95830,104406,113479,123063
%N a(n) = n*(14*n^2 - 21*n + 13)/6.
%D T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H Vincenzo Librandi, <a href="/A071229/b071229.txt">Table of n, a(n) for n = 0..2000</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*a(n-1) -6*a(n-2) +4*a(n-3) -1*a(n-4).
%F G.f.: x*(1 + 5*x + 8*x^2)/(1-x)^4. - _Harvey P. Dale_, Jun 29 2011
%F E.g.f.: (1/6)*x*(6 + 21*x + 14*x^2)*exp(x). - _G. C. Greubel_, Aug 05 2024
%t Table[ n*(14*n^2 - 21*n + 13)/6, {n, 0, 40}]
%t LinearRecurrence[{4,-6,4,-1},{0,1,9,38},40] (* or *) CoefficientList[ Series[x*(1+5x+8x^2)/(1-x)^4,{x,0,40}],x] (* _Harvey P. Dale_, Jun 29 2011 *)
%o (Magma) [n*(14*n^2-21*n+13)/6: n in [0..50]]; // _Vincenzo Librandi_, Jun 14 2011
%o (SageMath)
%o def A071229(n): return n*(14*n^2-21*n+13)/6
%o [A071229(n) for n in range(51)] # _G. C. Greubel_, Aug 05 2024
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 11 2002
%E More terms from _Robert G. Wilson v_, Jun 12 2002