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

0,2

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

Links

Table of n, a(n) for n=0..54.

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.

Example

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

Crossrefs

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

Sequence in context: A280789 A121468 A168151 * A180281 A187888 A239102

Adjacent sequences: A213218 A213219 A213220 * A213222 A213223 A213224

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 02 2013

Status

approved