|
%I #18 Dec 20 2023 16:00:34
%S 1,8,48,400,2288,20112,108016,1018256,5030640,51991696,229724144,
%T 2681810832,10182741232,139998665360,430234843632,7409690416528,
%U 16683460826864,398259202498704,536014603805680,21766500736121744
%N a(0) = 1, a(1) = 8, a(n) = 56*a(n-2) - a(n-1).
%C a(n)/a(n-1) tends to -8.
%H G. C. Greubel, <a href="/A165506/b165506.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 56).
%F G.f.: (1+9*x)/(1+x-56*x^2).
%F a(n) = Sum_{k=0..n} A112555(n,k)*7^k.
%F a(n) = (16*7^n-(-8)^n)/15. - _Klaus Brockhaus_, Sep 26 2009
%F E.g.f.: (16*exp(7*x) - exp(-8*x))/15. - _G. C. Greubel_, Oct 21 2018
%e a(20)=8250317076996336, a(21)=1210673724145821328, a(22)=-748655967834026512, a(23)=68546384520000020880, a(24)=-110471118718705505552,...
%t LinearRecurrence[{-1, 56}, {1, 8}, 50] (* _G. C. Greubel_, Oct 21 2018 *)
%t CoefficientList[Series[-(1+9x)/(56x^2-x-1),{x,0,20}],x] (* _Harvey P. Dale_, Dec 20 2023 *)
%o (PARI) vector(50, n, n--; (16*7^n-(-8)^n)/15) \\ _G. C. Greubel_, Oct 21 2018
%o (Magma) [(16*7^n-(-8)^n)/15: n in [0..50]]; // _G. C. Greubel_, Oct 21 2018
%K sign
%O 0,2
%A _Philippe Deléham_, Sep 21 2009
|
