A108286 -id:A108286 - cp's OEIS frontend

A108285 Triangle read by rows, generated from (1, 2, 3, ...).

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, 1, 9, 51, 194, 453, 543, 247, 36

Offset: 0

Gary W. Adamson, May 30 2005

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 5th 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.

Triangle A108243 is generated by analogous operations from (..., 3, 2, 1) instead of (1, 2, 3, ...).

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

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

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

cp's OEIS Frontend

A108285 Triangle read by rows, generated from (1, 2, 3, ...).

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