Consider the triangular numbers and their forward differences: $$ T = 1, 3, 6, 10, 15, 21, ... \\ \Delta T = 1,2,3,4,5,6, ... $$ If we alter \$\Delta T\$ so that it begins with a different integer, we get a different, yet similar sequence (assuming that it begins with \$T'_1 = 1\$): $$ \Delta T' ...