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A060933 Sixth convolution of Lucas numbers A000032(n+1), n >= 0.

%I A060933 #18 Apr 08 2021 04:13:13
%S A060933 1,21,217,1498,7910,34566,131446,449732,1416513,4174765,11651717,
%T A060933 31075422,79751854,198036146,477899790,1124785648,2589534248,
%U A060933 5845989156,12968091584,28316428700,60953528230,129515454530,271955244610,564879359940,1161646929275,2366938010983,4781794056543
%N A060933 Sixth convolution of Lucas numbers A000032(n+1), n >= 0.
%H A060933 Vincenzo Librandi, <a href="/A060933/b060933.txt">Table of n, a(n) for n = 0..1000</a>
%H A060933 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,-7,49,-14,-77,29,77,-14,-49,-7,14,7,1).
%F A060933 G.f.: ( (1+2*x) / (1-x-x^2) )^7.
%F A060933 a(n) = A060922(n+6, 6) (seventh column of Lucas triangle).
%F A060933 a(n) = (n+1)*(2*(100*n^5 +845*n^4 +2480*n^3 +4345*n^2 +5910*n +2952)*L(n+2) + (125*n^5 +1030*n^4 +2995*n^3 +5930*n^2 +8280*n +288)*L(n+1))/(6!*5^2), with the Lucas numbers L(n)=A000032(n).
%p A060933 m:= 40; S:= series( ((1+2*x)/(1-x-x^2))^7, x, m+1);
%p A060933 seq(coeff(S, x, j), j = 0..m); # _G. C. Greubel_, Apr 08 2021
%t A060933 Table[(n+1)(2(100n^5+845n^4+2480n^3+4345n^2+5910n+2952)LucasL[n+2]+(125n^5+ 1030n^4+2995n^3+5930n^2+8280n+288)LucasL[n+1])/18000,{n,0,30}] (* _Harvey P. Dale_, Aug 13 2013 *)
%t A060933 CoefficientList[Series[((1+2x)/(1-x-x^2))^7, {x,0,30}], x] (* _Vincenzo Librandi_, Aug 13 2013 *)
%o A060933 (Magma)
%o A060933 R<x>:=PowerSeriesRing(Integers(), 40);
%o A060933 Coefficients(R!( ((1+2*x)/(1-x-x^2))^7 )); // _G. C. Greubel_, Apr 08 2021
%o A060933 (Sage)
%o A060933 def A060930_list(prec):
%o A060933     P.<x> = PowerSeriesRing(ZZ, prec)
%o A060933     return P( ((1+2*x)/(1-x-x^2))^7 ).list()
%o A060933 A060930_list(40) # _G. C. Greubel_, Apr 08 2021
%Y A060933 Cf. A000032, A000204, A004799, A060922, A060929, A060930, A060931, A060932.
%K A060933 nonn,easy
%O A060933 0,2
%A A060933 _Wolfdieter Lang_, Apr 20 2001