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 A017125 #7 Mar 30 2012 18:51:18 %S A017125 0,1,1,1,1,2,2,2,1,3,3,3,3,1,4,5,5,4,4,1,5,8,8,7,5,5,1,6,13,13,11,9,6, %T A017125 6,1,7,21,21,18,14,11,7,7,1,8,34,34,29,23,17,13,8,8,1,9,55,55,47,37, %U A017125 28,20,15,9,9,1,10,89,89,76,60,45,33,23,17,10,10,1,11,144,144,123,97,73 %N A017125 Table read by antidiagonals of Fibonacci-type sequences. %F A017125 T(n, k) = T(n, k-1)+T(n, k-2) [with T(n, 0) = n and T(n, 1) = 1] = 2*T(n-1, k)-T(n-2, k) = Fib(k)+n*Fib(k-1) = (s^k*(1+2n/s)-t^k*(1+2n/t))/(2^k*sqrt(5)) where s = (1+sqrt(5))/2 and t = (1-sqrt(5))/2 = 1-s. %F A017125 G.f. for n-th row: (n+x-nx)/(1-x-x^2). %Y A017125 Rows are (essentially) A000045, A000045, A000032, A000285, A022095, A022096, A022097, etc. Columns are (essentially) A001477, A000012, A000027, A005408, A016789, A016885, etc. One of the diagonals is A007502. %Y A017125 Antidiagonal sums are in A019274. %K A017125 easy,nonn,tabl %O A017125 0,6 %A A017125 _Henry Bottomley_, Jul 31 2000