A213221 Riordan array (f(x), x*g(x)) where f(x) is the g.f. of A157004 and g(x) is the g.f. of A157003.

1, 2, 1, 6, 3, 1, 18, 10, 4, 1, 58, 32, 15, 5, 1, 192, 106, 52, 21, 6, 1, 650, 357, 180, 79, 28, 7, 1, 2232, 1222, 624, 288, 114, 36, 8, 1, 7746, 4230, 2178, 1035, 439, 158, 45, 9, 1, 27096, 14770, 7648, 3706, 1642, 643, 212, 55, 10, 1

Offset: 0

Author

Philippe Deléham, Mar 02 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins
1
2, 1
6, 3, 1
18, 10, 4, 1
58, 32, 15, 5, 1
192, 106, 52, 21, 6, 1
650, 357, 180, 79, 28, 7, 1
2232, 1222, 624, 288, 114, 36, 8, 1
7746, 4230, 2178, 1035, 439, 158, 45, 9, 1
27096, 14770, 7648, 3706, 1642, 643, 212, 55, 10, 1
95376, 51918, 27000, 13265, 6056, 2508, 911, 277, 66, 11, 1
337404, 183472, 95744, 47532, 22174, 9552, 3708, 1255, 354, 78, 12, 1
		

References

• Baccherini, D.; Merlini, D.; Sprugnoli, R. Binary words excluding a pattern and proper Riordan arrays. Discrete Math. 307 (2007), no. 9-10, 1021--1037. MR2292531 (2008a:05003). See page 1032. - N. J. A. Sloane, Mar 25 2014

Crossrefs

Cf. A157003, A157004 (column k=0), A261058 (column k=1).

Formula

Column k has g.f. ((1-sqrt(1-4*x+4*x^3))/(2*(1-x^2)))^k/sqrt(1-4*x+4*x^3).

T(n,0) = 2*T(n,1) - 2*T(n-2,1), T(n+1,k+1) = T(n,k) + T(n+1,k+2) - T(n-1,k+2) for n>=0.