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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified April 11 02:27 EDT 2021. Contains 342886 sequences. (Running on oeis4.)