This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080871 #16 Jun 11 2024 10:54:53
%S A080871 1,1,4,7,31,55,244,433,1921,3409,15124,26839,119071,211303,937444,
%T A080871 1663585,7380481,13097377,58106404,103115431,457470751,811826071,
%U A080871 3601659604,6391493137,28355806081,50320119025,223244789044
%N A080871 a(n)*a(n+3) - a(n+1)*a(n+2) = 3, given a(0)=a(1)=1, a(2)=4.
%H A080871 Seiichi Manyama, <a href="/A080871/b080871.txt">Table of n, a(n) for n = 0..2000</a>
%H A080871 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 8, 0, -1).
%F A080871 a(n) = (3 + a(n-1)*a(n-2))/a(n-3) for n>2.
%F A080871 G.f.: (-x^3 - 4*x^2 + x + 1)/(x^4 - 8*x^2 + 1)
%F A080871 a(n+4) = 8*a(n+2)-a(n). [_Richard Choulet_, Dec 04 2008]
%F A080871 a(n) = (0.25 + sqrt(10)/20)*(sqrt(4 + sqrt(15)))^n + (0.25 + sqrt(10)/20)*(sqrt(4 - sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - sqrt(4 + sqrt(15)))^n + ( - 1/20*10^(1/2) + 1/4)*( - (sqrt(4 - sqrt(15))))^n. [_Richard Choulet_, Dec 06 2008]
%t A080871 RecurrenceTable[{a[0]==a[1]==1,a[2]==4,a[n]==(3+a[n+1]a[n+2])/a[n+3]},a,{n,30}] (* _Harvey P. Dale_, Jun 08 2017 *)
%Y A080871 Cf. A001519, A079496, A080872, A080873, A080874, A080875.
%Y A080871 Bisections are A001091 and A070997.
%K A080871 nonn
%O A080871 0,3
%A A080871 _Paul D. Hanna_, Feb 22 2003