A292466 Triangle read by rows: T(n,k) = 4*T(n-1,k-1) + T(n,k-1) with T(2*m,0) = 0 and T(2*m+1,0) = 5^m.

0, 1, 1, 0, 4, 8, 5, 5, 21, 53, 0, 20, 40, 124, 336, 25, 25, 105, 265, 761, 2105, 0, 100, 200, 620, 1680, 4724, 13144, 125, 125, 525, 1325, 3805, 10525, 29421, 81997, 0, 500, 1000, 3100, 8400, 23620, 65720, 183404, 511392, 625, 625, 2625, 6625, 19025, 52625

Offset

0,5

Links

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

Formula

T(n+1,n)^2 - 5*T(n,n)^2 = 11^n.

Example

First few rows are:
    0;
    1,   1;
    0,   4,   8;
    5,   5,  21,   53;
    0,  20,  40,  124,  336;
   25,  25, 105,  265,  761,  2105;
    0, 100, 200,  620, 1680,  4724, 13144;
  125, 125, 525, 1325, 3805, 10525, 29421, 81997.
--------------------------------------------------------------
The diagonal is      {0, 1,  8,  53, 336, 2105, ...} and
the next diagonal is {1, 4, 21, 124, 761, 4724, ...}.
Two sequences have the following property:
     1^2 - 5*   0^2 = 1      (= 11^0),
     4^2 - 5*   1^2 = 11     (= 11^1),
    21^2 - 5*   8^2 = 121    (= 11^2),
   124^2 - 5*  53^2 = 1331   (= 11^3),
   761^2 - 5* 336^2 = 14641  (= 11^4),
  4724^2 - 5*2105^2 = 161051 (= 11^5),
  ...

Crossrefs

The diagonal of the triangle is A091870.

The next diagonal of the triangle is A108404.

T(n,k) = b*T(n-1,k-1) + T(n,k-1): A292789 (b=-3), A292495 (b=-2), A117918 and A228405 (b=1), A227418 (b=2), this sequence (b=4).

Sequence in context: A133921 A021210 A197849 * A246856 A113969 A155782

Adjacent sequences: A292463 A292464 A292465 * A292467 A292468 A292469

Keyword

nonn,tabl,look

Author

Seiichi Manyama, Sep 22 2017

Status

approved