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A239101
Riordan array read by rows, corresponding to array in A180562.
2
1, 2, 1, 4, 2, 1, 10, 5, 2, 1, 26, 13, 6, 2, 1, 70, 35, 16, 7, 2, 1, 192, 96, 45, 19, 8, 2, 1, 534, 267, 126, 56, 22, 9, 2, 1, 1500, 750, 357, 160, 68, 25, 10, 2, 1, 4246, 2123, 1016, 463, 198, 81, 28, 11, 2, 1, 12092, 6046, 2907, 1337, 586, 240, 95, 31
OFFSET
0,2
COMMENTS
Take lower triangle of square array in A180562, read from right to left.
Row sums are in A225034. - Philippe Deléham, Mar 25 2014
Riordan array (f(x), (f(x)-1)/(2*f(x))) where f(x) = sqrt((1+x)/(1-3*x)). - Philippe Deléham, Mar 25 2014
LINKS
D. Baccherini, D. Merlini, R. Sprugnoli, Binary words excluding a pattern and proper Riordan arrays, Discrete Math. 307 (2007), no. 9-10, 1021--1037. MR2292531 (2008a:05003).
FORMULA
T(0,0) = 1, T(n,0) = 2*T(n,1) for n>0, T(n,k) = T(n-1,k-1) - T(n-1,k) + T(n-1,k+1) + T(n,k+1) for k>0, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 25 2014
EXAMPLE
Triangle begins:
1
2 1
4 2 1
10 5 2 1
26 13 6 2 1
70 35 16 7 2 1
192 96 45 19 8 2 1
...
192 = 2*96, 96 = 70 - 35 + 16 + 45, 45 = 35 - 16 + 7 + 19, etc. - Philippe Deléham, Mar 25 2014
Production matrix is:
2, 1
0, 0, 1
2, 1, 0, 1
2, 1, 1, 0, 1
2, 1, 1, 1, 0, 1
2, 1, 1, 1, 1, 0, 1
2, 1, 1, 1, 1, 1, 0, 1
2, 1, 1, 1, 1, 1, 1, 0, 1
... Philippe Deléham, Sep 15 2014
CROSSREFS
Cf. A180562.
Cf. T(n,0) = A025565(n+1), T(n+1,1) = A005773(n+1), T(n+2,2) = A005717(n+1), A225034 (Row sums). - Philippe Deléham, Mar 25 2014
Sequence in context: A158982 A127124 A127136 * A362266 A145983 A245025
KEYWORD
nonn,tabl,more
AUTHOR
N. J. A. Sloane, Mar 25 2014
EXTENSIONS
More terms from Philippe Deléham, Mar 25 2014
STATUS
approved