cp's OEIS Frontend

A370176 a(n) = floor(x*a(n-1)) for n > 0 where x = 3+sqrt(15), a(0) = 1.

%I A370176 #16 Mar 31 2024 19:16:23
%S A370176 1,6,41,281,1931,13271,91211,626891,4308611,29613011,203529731,
%T A370176 1398856451,9614317091,66079041251,454160150051,3121435147811,
%U A370176 21453571787171,147450041609891,1013421680382371,6965230331953571,47871912074015651,329022854435815331,2261368599058985891
%N A370176 a(n) = floor(x*a(n-1)) for n > 0 where x = 3+sqrt(15), a(0) = 1.
%C A370176 x = A092294 = 3+sqrt(15) = 6.872983346...
%H A370176 Paolo Xausa, <a href="/A370176/b370176.txt">Table of n, a(n) for n = 0..1000</a>
%H A370176 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,0,-6).
%F A370176 a(n) = 7*a(n-1) - 6*a(n-3), a(0) = 1, a(1) = 6, a(2) = 41.
%F A370176 a(n) = 6*a(n-1) + 6*a(n-2) - 1.
%F A370176 a(n) = ((30-7*sqrt(15))*(3-sqrt(15))^n + (30+7*sqrt(15))*(3+sqrt(15))^n + 6)/66.
%F A370176 G.f.: (1-x-x^2)/(1-7*x+6*x^3).
%F A370176 a(n) = Sum_{k = 0..n} A370174(n,k)*5^k.
%F A370176 a(n) = (10*A057089(n) + 5*A057089(n-1) + 1)/11.
%e A370176 a(0) = 1;
%e A370176 a(1) = floor(x) = 6 where x = 3+sqrt(15);
%e A370176 a(2) = floor(6*x) = 41;
%e A370176 a(3) = floor(41*x) = 281.
%t A370176 NestList[Floor[(Sqrt[15]+3)*#] &, 1, 25] (* or *)
%t A370176 LinearRecurrence[{7, 0, -6}, {1, 6, 41}, 25] (* _Paolo Xausa_, Mar 31 2024 *)
%Y A370176 Cf. A057089, A092294, A370174.
%K A370176 nonn,easy
%O A370176 0,2
%A A370176 _Philippe Deléham_, Mar 19 2024