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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 20 22:20 EDT 2019. Contains 325189 sequences. (Running on oeis4.)