A239101 Riordan array read by rows, corresponding to array in A180562.

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

Table of n, a(n) for n=0..62.

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

Adjacent sequences: A239098 A239099 A239100 * A239102 A239103 A239104

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Mar 25 2014

Extensions

More terms from Philippe Deléham, Mar 25 2014

Status

approved