%I #19 Oct 18 2022 15:18:06
%S 8,792,4320,12650,27840,51948,87032,135150,198360,278720,378288,
%T 499122,643280,812820,1009800,1236278,1494312,1785960,2113280,2478330,
%U 2883168,3329852,3820440,4356990,4941560,5576208,6262992,7003970,7801200,8656740,9572648
%N a(n) = (7*n+1)*(7*n+2)*(7*n+4).
%H T. D. Noe, <a href="/A001547/b001547.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 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=8, a(1)=792, a(2)=4320, a(3)=12650. - _Harvey P. Dale_, Jan 12 2013
%F From _G. C. Greubel_, May 19 2019: (Start)
%F G.f.: 2*(4 + 380*x + 600*x^2 + 45*x^3)/(1 - x)^4.
%F E.g.f.: (8 + 784*x + 1372*x^2 + 343*x^3)*exp(x). (End)
%t Times@@@Table[7n+{1,2,4},{n,0,30}] (* or *) LinearRecurrence[{4,-6,4,-1},{8,792,4320,12650},40] (* _Harvey P. Dale_, Jan 12 2013 *)
%o (PARI) a(n) = (7*n+1)*(7*n+2)*(7*n+4); \\ _G. C. Greubel_, May 19 2019
%o (Magma) [(7*n+1)*(7*n+2)*(7*n+4): n in [0..30]]; // _G. C. Greubel_, May 19 2019
%o (Sage) [(7*n+1)*(7*n+2)*(7*n+4) for n in (0..30)] # _G. C. Greubel_, May 19 2019
%o (GAP) List([0..30], n-> (7*n+1)*(7*n+2)*(7*n+4)) # _G. C. Greubel_, May 19 2019
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_