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A236311
Riordan array ((1-x)/(1-3*x+3*x^2), x/(1-3*x+3*x^2)).
0
1, 2, 1, 3, 5, 1, 3, 15, 8, 1, 0, 33, 36, 11, 1, -9, 54, 117, 66, 14, 1, -27, 54, 297, 282, 105, 17, 1, -54, -27, 594, 945, 555, 153, 20, 1, -81, -297, 864, 2583, 2295, 963, 210, 23, 1, -81, -891, 513, 5778, 7803, 4725, 1533, 276, 26, 1, 0, -1863, -1944, 10098
OFFSET
0,2
COMMENTS
Row sums are 3^n = A000244(n).
Diagonals sums are 2^n = A000079(n).
T(n,n) = A000012(n).
T(n+1,n) = A016789(n).
T(n+2,n) = A062741(n+1).
T(n+3,n) = 3*A004188(n+1).
T(n,0) = A057682(n+1).
FORMULA
T(n,k) = 3*T(n-1,k) + T(n-1,k-1) -3*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k<0 or if k>n.
EXAMPLE
Triangle begins :
1;
2, 1;
3, 5, 1;
3, 15, 8, 1;
0, 33, 36, 11, 1;
-9, 54, 117, 66, 14, 1;
-27, 54, 297, 282, 105, 17, 1;
CROSSREFS
KEYWORD
easy,sign,tabl
AUTHOR
Philippe Deléham, Jan 21 2014
STATUS
approved