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%I #15 Oct 18 2022 15:17:54
%S 90,1560,6460,16848,34782,62320,101520,154440,223138,309672,416100,
%T 544480,696870,875328,1081912,1318680,1587690,1891000,2230668,2608752,
%U 3027310,3488400,3994080,4546408,5147442,5799240,6503860,7263360,8079798,8955232,9891720
%N a(n) = (7*n+3)*(7*n+5)*(7*n+6).
%H T. D. Noe, <a href="/A001561/b001561.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F From _G. C. Greubel_, Apr 28 2019: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: 2*(45 + 600*x + 380*x^2 + 4*x^3)/(1-x)^4.
%F E.g.f.: (90 + 1470*x + 1715*x^2 + 343*x^3)*exp(x). (End)
%t Table[(7*n+3)*(7*n+5)*(7*n+6), {n, 0, 40}] (* _T. D. Noe_, Aug 09 2012 *)
%t LinearRecurrence[{4,-6,4,-1},{90,1560,6460,16848},40] (* _Harvey P. Dale_, Sep 26 2021 *)
%o (PARI) a(n) = (7*n+3)*(7*n+5)*(7*n+6); \\ _G. C. Greubel_, Apr 28 2019
%o (Magma) [(7*n+3)*(7*n+5)*(7*n+6): n in [0..40]]; // _G. C. Greubel_, Apr 28 2019
%o (Sage) [(7*n+3)*(7*n+5)*(7*n+6) for n in range(40)] # _G. C. Greubel_, Apr 28 2019
%o (GAP) List([0..40], n-> (7*n+3)*(7*n+5)*(7*n+6)) # _G. C. Greubel_, Apr 28 2019
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_