A370178 - OEIS

%I #13 Apr 21 2024 19:13:12

%S 1,8,71,631,5615,49967,444655,3956975,35213039,313360111,2788585199,

%T 24815562479,220833181423,1965189951215,17488185061103,

%U 155627000098543,1384921481277167,12324387851005679,109674474658262767,975990900074147567,8685322997859282671

%N a(n) = floor(x*a(n-1)) for n > 0 where x = 4 + 2*sqrt(6), a(0) = 1.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,0,-8).

%F a(n) = 9*a(n-1) - 8*a(n-3) for n>2, a(0) = 1, a(1) = 8, a(2) = 71.

%F a(n) = 8*a(n-1) + 8*a(n-2) - 1.

%F G.f.: (1-x-x^2)/((1-x)*(1-8*x-8*x^2)).

%F a(n) = Sum_{k=0..n} A370174(n,k)*7^k.

%F a(n) = (7*(8-3*sqrt(6))*(4-2*sqrt(6))^n + 7*(8+3*sqrt(6))*(4+2*sqrt(6))^n + 8)/120.

%F a(n) = (14*A057091(n) + 7*A057091(n-1) + 1)/15.

%t LinearRecurrence[{9,0,-8},{1,8,71},21] (* _James C. McMahon_, Apr 21 2024 *)

%Y Cf. A057091, A090654 (x value), A370174.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Apr 02 2024