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 A177877 #19 Feb 09 2025 02:45:53 %S A177877 1,2,4,3,7,10,4,10,16,20,5,13,22,30,35,6,16,28,40,50,56,7,19,34,50,65, %T A177877 77,84,8,22,40,60,80,98,112,120,9,25,46,70,95,119,140,156,165,10,28, %U A177877 52,80,110,140,168,192,210,220 %N A177877 Triangle in which row n is derived from (1,2,3,...,n) dot (n,n-1,...,1) with additive carryovers. %C A177877 Carryovers (additive) are defined as "add current product to next product". For example: (1,2,3) dot (3,2,1) with carryovers = ((1*3=3), (2*2+3=7), (3*1+7=10)), so row 2 = (3, 7, 10). %F A177877 By rows, (1,2,3,...) dot (...3,2,1); add current product to next product. %F A177877 As an array, row 0 = the tetrahedral numbers, (1, 4, 10, 20, 35,...). n-th row adds n*(1, 3, 6, 10, 15,...) termwise. %e A177877 Row 2 = (3, 7, 10) = (1, 2, 3) dot (3, 2, 1) with carryovers, thus: (3 = 1*3; 7 = 2*2 + 3; 10 = 3*1 + 7). %e A177877 First few rows of the array: %e A177877 1, 4, 10, 20, 35,... %e A177877 2, 7, 16, 30, 50,... %e A177877 3, 10, 22, 40, 65,... %e A177877 ... %e A177877 Example: row 1 is obtained by adding (1, 3, 6, 10, 15,...) termwise to (1, 4, 10, 20, 35,...). %e A177877 First few rows of the triangle: %e A177877 1; %e A177877 2, 4; %e A177877 3, 7, 10; %e A177877 4, 10, 16, 20; %e A177877 5, 13, 22, 30, 35; %e A177877 6, 16, 28, 40, 50, 56; %e A177877 7, 19, 34, 50, 65, 77, 84; %e A177877 8, 22, 40, 60, 80, 98, 112, 120; %e A177877 9, 25, 46, 70, 95, 119, 140, 156, 165; %e A177877 10, 28, 52, 80, 110, 140, 168, 192, 210, 220; %e A177877 ... %Y A177877 Cf. A002415 (row sums). %K A177877 nonn,tabl,easy %O A177877 0,2 %A A177877 _Gary W. Adamson_, Dec 13 2010