A292495
Triangle read by rows: T(n,k) = (-2)*T(n-1,k-1) + T(n,k-1) with T(2*m,0) = 0 and T(2*m+1,0) = (-1)^m.
Original entry on oeis.org
0, 1, 1, 0, -2, -4, -1, -1, 3, 11, 0, 2, 4, -2, -24, 1, 1, -3, -11, -7, 41, 0, -2, -4, 2, 24, 38, -44, -1, -1, 3, 11, 7, -41, -117, -29, 0, 2, 4, -2, -24, -38, 44, 278, 336, 1, 1, -3, -11, -7, 41, 117, 29, -527, -1199, 0, -2, -4, 2, 24, 38, -44, -278, -336, 718
Offset: 0
First few rows are:
0;
1, 1;
0, -2, -4;
-1, -1, 3, 11;
0, 2, 4, -2, -24;
1, 1, -3, -11, -7, 41;
0, -2, -4, 2, 24, 38, -44;
-1, -1, 3, 11, 7, -41, -117, -29;
0, 2, 4, -2, -24, -38, 44, 278, 336.
The diagonal of the triangle is related to
A099456.
The next diagonal of the triangle is related to
A139011.
A292789
Triangle read by rows: T(n,k) = (-3)*T(n-1,k-1) + T(n,k-1) with T(2*m,0) = 0 and T(2*m+1,0) = (-2)^m.
Original entry on oeis.org
0, 1, 1, 0, -3, -6, -2, -2, 7, 25, 0, 6, 12, -9, -84, 4, 4, -14, -50, -23, 229, 0, -12, -24, 18, 168, 237, -450, -8, -8, 28, 100, 46, -458, -1169, 181, 0, 24, 48, -36, -336, -474, 900, 4407, 3864, 16, 16, -56, -200, -92, 916, 2338, -362, -13583, -25175, 0, -48
Offset: 0
First few rows are:
0;
1, 1;
0, -3, -6;
-2, -2, 7, 25;
0, 6, 12, -9, -84;
4, 4, -14, -50, -23, 229;
0, -12, -24, 18, 168, 237, -450;
-8, -8, 28, 100, 46, -458, -1169, 181;
0, 24, 48, -36, -336, -474, 900, 4407, 3864.
--------------------------------------------------------------
The diagonal is {0, 1, -6, 25, -84, ...} and
the next diagonal is {1, -3, 7, -9, -23, ...}.
Two sequences have the following property:
1^2 + 2* 0^2 = 1 (= 11^0),
(-3)^2 + 2* 1^2 = 11 (= 11^1),
7^2 + 2* (-6)^2 = 121 (= 11^2),
(-9)^2 + 2* 25^2 = 1331 (= 11^3),
(-23)^2 + 2*(-84)^2 = 14641 (= 11^4),
...