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 A106196 #10 Feb 13 2022 23:17:38 %S A106196 1,1,1,2,2,1,3,5,3,1,5,10,8,4,1,8,20,17,11,5,1,13,38,35,24,14,6,1,21, %T A106196 71,68,50,31,17,7,1 %N A106196 Triangle read by rows, generated from Pascal's triangle. %C A106196 The array P = %C A106196 1, 0, 0, 0, 0, 0, ... %C A106196 0, 1, 0, 0, 0, 0, ... %C A106196 0, 1, 1, 0, 0, 0, ... %C A106196 0, 0, 2, 1, 0, 0, ... %C A106196 0, 0, 1, 3, 1, 0, ... %C A106196 0, 0, 0, 3, 4, 1, ... %C A106196 ... %C A106196 ... as shown on page 107 of "A Primer for the Fibonacci Numbers". %C A106196 The array A is composed of arithmetic sequences, as a matrix. %C A106196 1, 1, 1, 1, 1, ... %C A106196 1, 2, 3, 4, 5, ... %C A106196 1, 3, 5, 7, 9, ... %C A106196 1, 4, 7, 10, 13, ... %C A106196 1, 5, 9, 13, 17, ... %C A106196 ... %C A106196 Leftmost column = Fibonacci numbers, next column (1, 2, 5, 10, 20, ...) = Fibonacci numbers convolved with themselves. %D A106196 V. E. Hoggatt, Jr., editor; "A Primer for the Fibonacci Numbers", 1963, p. 107. %F A106196 Let P = an array with columns composed of Pascal's Triangle rows, offset, spaces filled in with zeros; A = an array composed of arithmetic sequences(n, k). Perform P * A and extract antidiagonals which become the rows of A106196. %e A106196 The operation P * A generates the array: %e A106196 1, 1, 1, 1, 1, ... %e A106196 1, 2, 3, 4, 5, ... %e A106196 2, 5, 8, 11, 14, ... %e A106196 3, 10, 17, 24, 31, ... %e A106196 5, 20, 35, 50, 65, ... %e A106196 ... %e A106196 from which we extract antidiagonals, read by rows, become triangle A106196: %e A106196 1; %e A106196 1, 1; %e A106196 2, 2, 1; %e A106196 3, 5, 3, 1; %e A106196 5, 10, 8, 4, 1; %e A106196 8, 20, 17, 11, 5, 1; %e A106196 13, 38, 35, 24, 14, 6, 1; %e A106196 21, 71, 68, 50, 31, 17, 7, 1; %e A106196 ... %Y A106196 Cf. A052996, A007678, A106196. %K A106196 nonn,tabl %O A106196 0,4 %A A106196 _Gary W. Adamson_, Apr 24 2005