0,3

By diagonals (d=1,2,3...) going to the left with (1,3,6...) = d(1), these are sequences of the form (k-th term a(k) = d*a(k-1) + k). Example: 1, 7, 38, 194...(the 5-th diagonal) = A014827,is generated by a(k) = 5*a(k-1) + k. Diagonal 2 = (1, 4, 11, 26...) = A000295; Diagonal 3 = (1, 5, 18...) = A000340; Diagonal 4 = (1, 6, 27...) = A014825. First few rows of the triangle are: 1; 1, 3 1, 4, 6; 1, 5, 11, 10; 1, 6, 18, 26, 15; 1, 7, 27, 58, 57, 21; 1, 8, 38, 112, 179, 120, 28; ... Triangle A108243 is generated by analogous operations from (...3, 2, 1) instead of (l, 2, 3...)

n-th column = f(x), x = 1, 2, 3...; x^(n) + 2*x^(n-1) + 3*x^(n-2) + ...+ (n+1).

4-th column (offset) = 10, 26, 58, 112...= f(x), x = 1, 2, 3; x^3 + 2x^2 + 3x + 4.

Cf. A108286, A000295, A000349, A014825, A000217, A108283, A108284, A108286.

Adjacent sequences: A108282 A108283 A108284 this_sequence A108286 A108287 A108288

Sequence in context: A051203 A086271 A080851 this_sequence A075419 A060922 A143790

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2005