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
Examples
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),
...
Links
- Seiichi Manyama, Rows n = 0..139, flattened
Crossrefs
Formula
T(n+1,n)^2 - 5*T(n,n)^2 = 11^n.