STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A209137
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Triangle of coefficients of polynomials u(n,x) jointly generated with A209138; see the Formula section.
(history; published version)
(history; published version)
STATUS
editing
proposed
COMMENTS
alternating Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...
Subtriangle of the triangle given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Apr 11 2012
FORMULA
u(n,x) = u(n-1,x) + (x+1)*v(n-1,x),
v(n,x) = (x+1)*u(n-1,x) + x*v(n-1,x),
Contribution from _From _Philippe Deléham_, Apr 11 2012. : (Start)
As DELTA-triangle T(n,k) with 0 <= k <= n :
T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + T(n-2,k-2), T(0,0) = T(1,0) = T(2,1) = 1, T(2,0) = 2, T(1,1) = T(2,2) = 0 and T(n,k) = 0 if k < 0 or if k > n. (End)
EXAMPLE
1;
2..., 1;
3..., 4...., 2;
5..., 10..., 9...., 3;
8..., 22..., 28..., 18..., 5;
First three polynomials u(n,x): 1, 2 + x, 3 + 4x + 2x^2
1
2 + x
3 + 4x + 2x^2
From Philippe Deléham, Apr 11 2012: (Start)
(1, 1, -1, 0, 0, 0, ...) DELTA (0, 1, 1, -1, 0, 0, 0, ...) begins :
1;
1, 0;
2, 1, 0;
3, 4, 2, 0;
5, 10, 9, 3, 0;
8, 22, 28, 18, 5, 0;
13, 45, 74, 68, 35, 8, 0 .- _Philippe Deléham_, Apr 11 2012; (End)
STATUS
approved
editing
COMMENTS
Mirror image of triangle in A209138. - _Philippe Deléham, _, Apr 11 2012
FORMULA
Contribution from _Philippe Deléham, _, Apr 11 2012. (Start)
EXAMPLE
13, 45, 74, 68, 35, 8, 0 .- _Philippe Deléham, _, Apr 11 2012
COMMENTS
Subtriangle of the triangle given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.- DELEHAM _Philippe, Deléham_, Apr 11 2012
STATUS
editing
approved
COMMENTS
Subtriangle of the triangle given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.- DELEHAM Phiippe, Philippe, Apr 11 2012
STATUS
approved
editing
COMMENTS
Mirror image of triangle in A209138. - DELEHAM Philippe, Deléham, Apr 11 2012
FORMULA
Contribution from DELEHAM Philippe, Deléham, Apr 11 2012. (Start)
EXAMPLE
13, 45, 74, 68, 35, 8, 0 .- DELEHAM Philippe, Deléham, Apr 11 2012
COMMENTS
u(n,1) = nth n-th row sum = 3^(n-1).
STATUS
proposed
approved