|
%I #17 Sep 29 2023 10:17:24
%S 1,4,18,87,431,2150,10744,53713,268557,1342776,6713870,33569339,
%T 167846683,839233402,4196166996,20980834965,104904174809,524520874028,
%U 2622604370122,13113021850591,65565109252935,327825546264654
%N a(n+1) = 5*a(n) - n.
%H G. C. Greubel, <a href="/A164045/b164045.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -11, 5).
%F a(0)=1; a(n+1) = 5*a(n) - n.
%F a(n) = (11*5^n + 4*n + 5)/16.
%F From _R. J. Mathar_, Aug 09 2009: (Start)
%F a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).
%F G.f.: (1-3*x+x^2)/((1-5*x)*(1-x)^2). (End)
%F E.g.f.: (1/16)*(11*exp(5*x) + (4*x + 5)*exp(x)). - _G. C. Greubel_, Sep 08 2017
%t Table[(11*5^n + 4*n + 5)/16, {n,0,50}] (* _G. C. Greubel_, Sep 08 2017 *)
%t LinearRecurrence[{7,-11,5},{1,4,18},30] (* or *) nxt[{n_,a_}]:={n+1,5a-n-1}; NestList[nxt,{0,1},30][[;;,2]] (* _Harvey P. Dale_, Sep 29 2023 *)
%o (PARI) a(n) = (11*5^n + 4*n + 5)/16 \\ _Michel Marcus_, Jul 18 2013
%K nonn
%O 0,2
%A _Rolf Pleisch_, Aug 08 2009
|
