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a(n) = (7*n+3)*(7*n+5)*(7*n+6).
1

%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_