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.

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

0,5

Links

Seiichi Manyama, Rows n = 0..139, flattened

Formula

T(n+1,n)^2 + 2*T(n,n)^2 = 11^n.

Example

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),
  ...

Crossrefs

T(n,k) = b*T(n-1,k-1) + T(n,k-1): this sequence (b=-3), A292495 (b=-2), A117918 and A228405 (b=1), A227418 (b=2), A292466 (b=4).

Sequence in context: A120907 A133358 A058099 * A124085 A132120 A021280

Adjacent sequences: A292786 A292787 A292788 * A292790 A292791 A292792

Keyword

sign,tabl

Author

Seiichi Manyama, Sep 23 2017

Status

approved