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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 (list; table; graph; refs; listen; history; text; internal format)
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 * A145983 A245025 A257495

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

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Last modified April 18 16:45 EDT 2019. Contains 322209 sequences. (Running on oeis4.)