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 A271355 #11 Nov 17 2024 21:38:51
%S A271355 1,2,1,3,2,1,4,3,2,1,7,4,3,2,1,11,7,4,3,2,1,18,11,7,4,3,2,1,29,18,11,
%T A271355 7,4,3,2,1,47,29,18,11,7,4,3,2,1,76,47,29,18,11,7,4,3,2,1,123,76,47,
%U A271355 29,18,11,7,4,3,2,1,199,123,76,47,29,18,11,7,4,3
%N A271355 Triangular array: T(n,k) = |round((r^n)*(s^k))|, where r = golden ratio = (1+sqrt(5))/2, s = (1-sqrt(5))/2, 1 <= k <= n, n >= 1.
%C A271355 Row n consists of the first n numbers of A169985 = (1,2,3,4,7,... ) in reverse order; these are the Lucas numbers, A000032, with order of initial two terms reversed. Every column of the triangle is A169985.
%H A271355 Clark Kimberling, <a href="/A271355/b271355.txt">Table of n, a(n) for n = 1..10000</a>
%F A271355 T(n,k) = |round((r^n)*(s^k))|, where r = golden ratio = (1+sqrt(5))/2, s = (1-sqrt(5))/2, 1 <= k <= n, n >= 1.
%F A271355 T(k+j-1,j) = A000032(k) = k-th Lucas number, for k >= 2.
%e A271355 First six rows:
%e A271355 1
%e A271355 2 1
%e A271355 3 2 1
%e A271355 4 3 2 1
%e A271355 7 4 3 2 1
%e A271355 11 7 4 3 2 1
%t A271355 r = N[(1 + Sqrt[5])/2, 100]; s = N[(1 - Sqrt[5])/2, 100];
%t A271355 t = Table[Abs[Round[(r^n)*(s^k)]], {n, 0, 15}, {k, 1, n}];
%t A271355 Flatten[t] (* A271355, sequence *)
%t A271355 TableForm[t] (* A271355, array *)
%Y A271355 Cf. A169985, A000032, A000045, A104762
%K A271355 nonn,easy,tabl
%O A271355 1,2
%A A271355 _Clark Kimberling_, May 01 2016