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 A095003 #17 Nov 12 2022 18:24:59
%S A095003 1,6,45,352,2769,21798,171613,1351104,10637217,83746630,659335821,
%T A095003 5190939936,40868183665,321754529382,2533168051389,19943589881728,
%U A095003 157015551002433,1236180818137734,9732430994099437,76623267134657760,603253706083162641,4749406381530643366
%N A095003 a(n) = 9*a(n-1) - 9*a(n-2) + a(n-3).
%C A095003 a(n)/a(n-1) tends to 7.87298... = 4 + sqrt(15) = C (having the property that C + 1/C = 8). Eigenvalues of M are C, 1/C, 1; being roots of x^3 - 9x^2 + 9x - 1.
%H A095003 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-9,1).
%F A095003 a(n+3) = 9*a(n+2) - 9*a(n+1) + a(n); given a(1) = 1, a(2) = 6, a(3) = 45.
%F A095003 Let M be the 3 X 3 matrix [1 1 1 / 1 2 3 / 1 3 6]. M^n * [1 0 0] = [A095002(n) a(n) A095004(n)].
%e A095003 a(4) = 352 since M^4 * [1 0 0] = [145, 352, 640].
%p A095003 a:= n-> (<<1|1|1>, <1|2|3>, <1|3|6>>^n)[1, 2]:
%p A095003 seq(a(n), n=1..23); # _Alois P. Heinz_, Jun 06 2021
%t A095003 a[n_] := (MatrixPower[{{1, 1, 1}, {1, 2, 3}, {1, 3, 6}}, n].{{1}, {0}, {0}})[[2, 1]]; Table[ a[n], {n, 20}]; (* _Robert G. Wilson v_, May 29 2004 *)
%t A095003 LinearRecurrence[{9,-9,1},{1,6,45},30] (* _Harvey P. Dale_, Nov 12 2022 *)
%Y A095003 Cf. A095002, A095004, A076765.
%K A095003 nonn
%O A095003 1,2
%A A095003 _Gary W. Adamson_, May 27 2004
%E A095003 Edited and extended by _Robert G. Wilson v_, May 29 2004
%E A095003 Definition corrected and edited by _Georg Fischer_, Jun 06 2021