A136018 Triangle read by rows: r(n,k) = g(n,n-k), where g(n,k) is the number of ideals of size k in a garland (or double fence) of order n (see A137278).

1, 1, 1, 1, 2, 1, 3, 3, 3, 1, 7, 6, 6, 4, 1, 15, 14, 12, 10, 5, 1, 33, 32, 27, 22, 15, 6, 1, 75, 72, 63, 50, 37, 21, 7, 1, 171, 164, 146, 118, 88, 58, 28, 8, 1, 391, 377, 338, 280, 212, 147, 86, 36, 9, 1, 899, 870, 786, 662, 514, 366, 234, 122, 45, 10, 1, 2077, 2014, 1834, 1564

Offset

0,5

Comments

Row n has n+1 terms.

References

T. S. Blyth, J. C. Varlet, Ockham algebras, Oxford Science Pub. 1994.

E. Munarini, Enumeration of order ideals of a garland, Ars Combin. 76 (2005), 185--192.

Links

Emanuele Munarini, Mar 21 2008, Table of n, a(n) for n = 0..495

Formula

Recurrence: r(n+3,k+1) = r(n+2,k) + r(n+2,k+1) + r(n+2,k+2) - r(n+1,k+1) - r(n,k+1).

Riordan matrix: R = ( g(x), f(x) ), where g(x) = ( 1 - x^2 )/sqrt( 1 - 2 x - x^2 - x^4 + 2 x^5 + x^6 ) f(x) = ( 1 - x + x^2 + x^3 - sqrt( 1 - 2 x - x^2 - 3 x^4 + 2 x^5 + x^6 ) )/(2x) g(x) is the generating series for the central ideals c(n) = g(2n,n). f(x)/x is the generating series for sequence A004149.

Crossrefs

Sequence in context: A178244 A227532 A152534 * A138022 A113278 A132382

Adjacent sequences: A136015 A136016 A136017 * A136019 A136020 A136021

Keyword

easy,nonn,tabl,look

Author

Emanuele Munarini, Mar 21 2008

Status

approved